A high-precision pi calculator that uses entirely batch commands.

#1
I found this example, which does not work with TCC, but works with CMD.
Code:
@if defined talk (echo on) else (echo off)
setlocal EnableDelayedExpansion
echo.pi.bat  -  By Don Cross  -  http://cosinekitty.com
set /a NumQuads = 30
set /a MaxQuadIndex = NumQuads - 1

echo.
echo.%time% - started
echo.

call :PiEngine 48 18 32 57 -20 239
call :PiEngine 16 5 -4 239
goto :EOF

:PiEngine
    call :SetToInteger Pi 0
    set Formula=
    :PiTermLoop
        if "%1" == "" (
            call :Print pi
            echo.
            echo.!time! - finished !Formula!
            echo.
            goto :EOF
        )
        call :ArctanRecip PiTerm %2
        set /a PiEngineFactor=%1
        if !PiEngineFactor! lss 0 (
            set /a PiEngineFactor *= -1
            set Formula=!Formula!
            call :MultiplyByInteger PiTerm !PiEngineFactor!
            call :Subtract Pi PiTerm
            set Operator=-
        ) else (
            call :MultiplyByInteger PiTerm %1
            call :Add Pi PiTerm
            set Operator=+
        )
        if defined Formula (
            set Formula=!Formula! !Operator! !PiEngineFactor!*arctan^(1/%2^)
        ) else (
            set Formula=pi = %1*arctan^(1/%2^)
        )
        shift
        shift
    goto PiTermLoop
    
:SetToInteger
    for /L %%i in (0, 1, !MaxQuadIndex!) do (
        set /a %1_%%i = 0
    )
    set /a %1_!MaxQuadIndex! = %2
    goto :EOF
    
:Print
    set PrintBuffer=x
    REM  Omit a couple of least significant quads, because they will have roundoff errors.
    if defined PiDebug (
        set /a PrintMinQuadIndex=0
    ) else (
        set /a PrintMinQuadIndex=2
    )
    set /a PrintMaxQuadIndex = MaxQuadIndex - 1
    for /L %%i in (!PrintMinQuadIndex!, 1, !PrintMaxQuadIndex!) do (
        set PrintDigit=!%1_%%i!
        if !PrintDigit! lss 1000 (
            if !PrintDigit! lss 100 (
                if !PrintDigit! lss 10 (
                    set PrintDigit=000!PrintDigit!
                ) else (
                    set PrintDigit=00!PrintDigit!
                )
            ) else (
                set PrintDigit=0!PrintDigit!
            )
        )
        set PrintBuffer=!PrintDigit!!PrintBuffer!
    )
    set PrintBuffer=!%1_%MaxQuadIndex%!.!PrintBuffer:x=!
    echo.%1 = !PrintBuffer!
    goto :EOF
    
:DivideByInteger
    if defined PiDebug echo.DivideByInteger %1 %2
    set /a DBI_Carry = 0
    for /L %%i in (!MaxQuadIndex!, -1, 0) do (
        set /a DBI_Digit = DBI_Carry*10000 + %1_%%i
        set /a DBI_Carry = DBI_Digit %% %2
        set /a %1_%%i = DBI_Digit / %2
    )
    goto :EOF
    
:MultiplyByInteger
    if defined PiDebug echo.MultiplyByInteger %1 %2
    set /a MBI_Carry = 0
    for /L %%i in (0, 1, !MaxQuadIndex!) do (
        set /a MBI_Digit = %1_%%i * %2 + MBI_Carry
        set /a %1_%%i = MBI_Digit %% 10000
        set /a MBI_Carry = MBI_Digit / 10000
    )
    goto :EOF   
    
:ArctanRecip
    if defined PiDebug echo.ArctanRecip %1 %2
    call :SetToInteger %1 1
    call :DivideByInteger %1 %2
    call :CopyValue AR_Recip %1
    set /a AR_Toggle = -1   
    set /a AR_K = 3
    :ArctanLoop
        if defined PiDebug (
            echo.
            echo.ArctanRecip  AR_K=!AR_K!    ---------------------------------------------------------
        )
        call :DivideByInteger AR_Recip %2
        call :DivideByInteger AR_Recip %2
        call :CopyValue AR_Term AR_Recip
        call :DivideByInteger AR_Term !AR_K!
        call :CopyValue AR_PrevSum %1
        if !AR_Toggle! lss 0 (
            call :Subtract %1 AR_Term
        ) else (
            call :Add %1 AR_Term
        )
        call :Compare AR_EqualFlag %1 AR_PrevSum
        if !AR_EqualFlag! == true goto :EOF
        set /a AR_K += 2
        set /a AR_Toggle *= -1
    goto ArctanLoop
    
:CopyValue
    if defined PiDebug echo.CopyValue %1 %2
    for /L %%i in (0, 1, !MaxQuadIndex!) do (
        set /a %1_%%i = %2_%%i
    )
    goto :EOF
    
:Add
    if defined PiDebug echo.Add %1 %2
    if defined PiDebug call :Print %1
    if defined PiDebug call :Print %2
    set /a Add_Carry = 0
    for /L %%i in (0, 1, !MaxQuadIndex!) do (
        set /a Add_Digit = Add_Carry + %1_%%i + %2_%%i
        set /a %1_%%i = Add_Digit %% 10000
        set /a Add_Carry = Add_Digit / 10000
    )
    goto :EOF   

:Subtract
    if defined PiDebug echo.Subtract %1 %2
    if defined PiDebug call :Print %1
    if defined PiDebug call :Print %2
    set /a Subtract_Borrow = 0
    for /L %%i in (0, 1, !MaxQuadIndex!) do (
        set /a Subtract_Digit = %1_%%i - %2_%%i - Subtract_Borrow
        if !Subtract_Digit! lss 0 (
            set /a Subtract_Digit += 10000
            set /a Subtract_Borrow = 1
        ) else (
            set /a Subtract_Borrow = 0
        )
        set /a %1_%%i = Subtract_Digit
    )
    goto :EOF   
    
:Compare
    if defined PiDebug echo.Compare %1 %2 %3
    if defined PiDebug call :Print %2
    if defined PiDebug call :Print %3
    set /a Compare_Index = 0
    set %1=true
    :CompareLoop
        if not !%2_%Compare_Index%! == !%3_%Compare_Index%! (
            if defined PiDebug echo.!%2_%Compare_Index%! neq !%3_%Compare_Index%!
            set %1=false
            goto :EOF
        )
        set /a Compare_Index += 1
        if !Compare_Index! gtr !MaxQuadIndex! (
            if defined PiDebug echo.Compare equal
            goto :EOF
        )
    goto CompareLoop   
    
REM    $Log: pi.bat,v $
REM    Revision 1.2  2007/09/06 21:49:15  Don.Cross
REM    Added time stamps and display of formula.
REM
REM    Revision 1.1  2007/09/06 21:12:36  Don.Cross
REM    Batch file for calculating pi
REM
Joe
 

samintz

Scott Mintz
May 20, 2008
1,284
11
Solon, OH, USA
#2
I also noticed that when I run this under TCC/Tcmd, that neither Ctrl+C nor Ctrl+Break actually stop execution of the script.

I have to hit Ctrl+Break multiple times to interrupt the script and stop it.
 
#4
On my Windows 7 x64 system, running CMD.EXE 64-bit or CMD.EXE 32-bit, this is what I get;
Code:
c:\utils>pi.cmd
pi.bat  -  By Don Cross  -  http://cosinekitty.com

17:37:37.85 - started

pi = 3.141592653589793238462643383279502884197169399375105820974944592307816406286208998628034825342117067982148086

17:37:41.25 - finished pi = 48*arctan(1/18) + 32*arctan(1/57) - 20*arctan(1/239)

pi = 3.141592653589793238462643383279502884197169399375105820974944592307816406286208998628034825342117067982148086

17:37:44.75 - finished pi = 16*arctan(1/5) - 4*arctan(1/239)
TCC 18.00.32 x64 returns;
Code:
c:\users\jlc\utils>pi.cmd
pi.bat  -  By Don Cross  -  http://cosinekitty.com

17:39:58.88 - started

MAPM Warning: 'M_apm_sdivide', Divide by 0
TCC: C:\Users\jlc\utils\pi.cmd [90]  Divide by zero " DBI_Digit /"
TCC-RT 21.01.49 x64 returns;
Code:
c:\users\jlc\utils>"C:\Program Files\JPSoft\TCC_RT_21\tcc.exe" /I /Q /C pi.cmd
pi.bat  -  By Don Cross  -  http://cosinekitty.com

17:41:28.66 - started

TCC: C:\Users\jlc\utils\pi.cmd [90]  Divide by zero " DBI_Digit %"
TCC: C:\Users\jlc\utils\pi.cmd [90]  Divide by zero " DBI_Digit /"
Joe
 

rconn

Administrator
Staff member
May 14, 2008
10,573
97
#5
I am impressed that the author was able to beat CMD into producing these results. And saddened that he wasted days of his life doing it.

The same result of his 195-line CMD batch file can be done in 1 line in TCC:

echo pi = %@eval[pi=0.108]

Or if you want a really high resolution pi:

echo pi=%@eval[pi=0.10000]

TCC calculating pi to 10,000 decimal places runs about 600 times faster than the CMD batch file calculating it to 108 places.

And the reason the batch file doesn't run in TCC is because of invalid syntax in his SET /A statements. Which CMD is rewriting internally to the correct format, which is (1) undocumented, and (2) inconsistent with how it parses SET statements without the /A. But I have made a change for 21.01.50 to emulate this undocumented behavior. Who knows, it might even be a CMD "feature".