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@echo off
:: define info header
::
   ::
   :: macros loaded into memory by this batch file:
   ::  - $str2float
   ::  - $float2str
   ::  - $floatAdd
   ::  - $floatSub
   ::  - $floatMul
   ::  - $intToHex
   ::

   ::
   :: supported modes of operation:
   :: ---------------------------------------------+---+---+---+---
   ::   extensions             (e/d: en/disabled)  | e | e | e | d
   ::   delayed expansion      (e/d: en/disabled)  | e | d | d |e/d
   ::   run from command line  (y/n:      yes/no)  |y/n| y | n |y/n
   :: ---------------------------------------------+---+---+---+---
   ::   macro behaviour    (l/e: load/executable)  |l+e| l |l+e| -
   ::

   ::
   :: This batch uses the following environment variable names
   :: of the current context, and will finally undefine them:
   ::  - bOR
   ::  - #
   ::

   ::
   :: rounding is applied to all floating point macros:
   ::
   :: Rounding to integers using the IEEE 754 rules
   :: No Rounding mode                                +2.5 +1.5 -1.5 -2.5
   :: 0  to nearest, ties to even           (default) +2.0 +2.0 -2.0 -2.0
   :: 1  to nearest, ties away from zero              +3.0 +2.0 -2.0 -3.0
   :: 2  toward 0           (truncation, no rounding) +2.0 +1.0 -1.0 -2.0
   :: 3  toward +inf        (rounding up, or ceiling) +3.0 +2.0 -1.0 -2.0
   :: 4  toward -inf        (rounding down, or floor) +2.0 +1.0 -2.0 -3.0
   ::
   :: you select a rounding mode by setting up the environment variable
   :: "roundingMode" with the number of the rounding mode.
   :: If none is selected, then the default is rounding mode 0.
   ::

   :: 
   :: some test cases:
   :: %$str2float% "10"
   :: %$str2float% "4"
   :: %$floatAdd%  "1092616192" "1082130432"
   :: %$float2str% "1096810496"
   :: %$floatSub%  "1092616192" "1082130432"
   :: %$float2str% "1086324736"
   :: %$floatMul%  "1092616192" "1082130432"
   :: %$float2str% "1109393408"
   :: %$intToHex%  "305419896"
   :: 
::
:: end define info header


:: define check for valid system state
::
:: If the extensions are disabled, the set command throws an "syntax error",
:: when assigning an equal sign ('='):
:: This is essential for complex macros, so the extensions MUST be enabled.
::
2> nul set "extensionsEnabled=true" || (
   echo(Error: The extensions are disabled, no macro will be loaded into memory.

   rem simulate: exit /b 1
   rem if extensions are disabled the label :EOF is not found
   call
   goto exit
)
::
:: end define check for valid system state
:: extensions enabled


:: define $str2float
::   %~1 float string
::   %~2 variable to store the resulting int coding of the float
::   actually there is only few error detection,
::   so assumed: no errorneous strings
::   set "inf=0x7F800000"
::   set "nan=0x7FFFFFFF"
::   NaN(...), +NaN(...), -NaN(...) format: NaN, +NaN, -NaN watched
::   "", "+", "NaN", "+NaN" ->  NaN == 0x7FFFFFFF == 2147483647
::   "-", "-NaN"            -> -NaN == 0xFFFFFFFF == -1
::   "inf", "+inf"          ->  inf == 0x7F800000 == 2139095040
::   "-inf"                 -> -inf == 0xFF800000 == -8388608
::
   (set #=0)
   if "!#!" == "0" (set bOR=^^^^) else (set bOR=^^)
   if "!#!" == "0" (set #=^^^^^^^^^^^^^^^!) else (set #=!)

   setlocal enableExtensions disableDelayedExpansion
   set LF=^


   set ^"\n=^^^%LF%%LF%^%LF%%LF%^<nul ^^^"
   set ^"[=%%~#^<nul ^^^%LF%%LF%^<nul ^^^"
   set ^"]=^<nul^^^%LF%%LF%^%LF%%LF%^<nul ^^^"
   endlocal & (

for %%# in ("") do set $str2float=@for %%N in ^(0 1^) do @if %%~N == 1 ^(%\n%
%[%
::"   parse params:"^
::"   first  token (mandatory) := float in string representation"^
::"   second token (optional)  := if present then use variable to store the result to, else use STDOUT"^
%]%
   set "N=0"%\n%
   set "param[1]= "%\n%
   set "param[2]= "%\n%
   for %%P in ^(%#%params%#%^) do @^(%\n%
      ^>nul set /A "N+=1"%\n%
      set ^"param[%#%N%#%]= %%~P^"%\n%
   ^)%\n%
   set "N="%\n%
%[%
::"   divide in parts: sPart * iPart.fPart * 10^^ePart"^
%]%
   set ^"string=%#%param[1]%#%^"%\n%
   set ^"string= %#%string: =%#%^"%\n%
   set "float="%\n%
   %\n%
   set ^"ePart=%#%string:*e=%#%^"%\n%
   if not defined ePart ^(%\n%
      set "ePart=e"%\n%
      set ^"string=%#%string:e=%#%^"%\n%
   ^) else if ^"%#%string%#%^" == ^"%#%ePart%#%^" ^(%\n%
      set "ePart=0"%\n%
   ^) else ^(%\n%
      for %%a in ^(^"%#%ePart%#%^"^) do @set ^"string=%#%string:e%%~a=%#%^"%\n%
   ^)%\n%
   %\n%
   set ^"fPart=%#%string:*.=%#%^"%\n%
   if not defined fPart ^(%\n%
      set "fPart=f"%\n%
      set ^"string=%#%string:.=%#%^"%\n%
   ^) else if ^"%#%string%#%^" == ^"%#%fPart%#%^" ^(%\n%
      set "fPart=0"%\n%
   ^) else ^(%\n%
      for %%a in ^(^"%#%fPart%#%^"^) do @set ^"string=%#%string:.%%~a=%#%^"%\n%
   ^)%\n%
   %\n%
   if ^"%#%string:~1,1%#%^" == "-" ^(%\n%
      set ^"iPart=%#%string:~2%#%^"%\n%
      set "sPart=-"%\n%
   ^) else if ^"%#%string:~1,1%#%^" == "+" ^(%\n%
      set ^"iPart=%#%string:~2%#%^"%\n%
      set "sPart="%\n%
   ^) else ^(%\n%
      set ^"iPart=%#%string:~1%#%^"%\n%
      set "sPart="%\n%
   ^)%\n%
   if not defined iPart set "iPart=i"%\n%
%[%
::"   set sign flag (s)"^
%]%
   if defined sPart ^( ^>nul set /A "s=1<<31" ^) else ^( set "s=0" ^)%\n%
%[%
::"   detect NaN, inf and hex format"^
%]%
   if ^"%#%iPart:~0,3%#%^" == "NaN" ^(%\n%
      for /F "tokens=1,2 delims=+-() " %%a in ^(^"%#%param[1]%#%^"^) do @^(%\n%
         if "%%~b" == "" ^(%\n%
            ^>nul set /A "float=s|0x7FFFFFFF"%\n%
         ^) else ^(%\n%
            set    "float=%%~b"%\n%
            ^>nul set /A ^"float=^(0x%#%float:~0,1%#%^<^<28^)+0x%#%float:~1%#%^"%\n%
            ^>nul set /A "float=s%bOR%float"%\n%
         ^)%\n%
      ^)%\n%
   ^) else if ^"%#%iPart:~0,3%#%^" == "inf" ^( ^>nul set /A "float=s|0x7F800000"%\n%
   ^) else if ^"%#%iPart:~0,2%#%^" == "0x" ^( ^>nul set /A "float=s%bOR%iPart"%\n%
   ^) else if ^"%#%iPart%#%%#%fPart%#%^" == "if" ^( ^>nul set /A "float=s|0x7FFFFFFF"%\n%
   ^) else if ^"%#%ePart%#%^" == "e" ^( ^>nul set /A "float=s|0x7FFFFFFF"%\n%
   ^) else ^(%\n%
%[%
::"   normalize to: sPart * 0.significand * 10^ePart, 0.significand >= 0.1"^
::"   AND"^
::"   detect 0.0"^
%]%
      for /F "tokens=* delims= " %%a in ^(^"%#%iPart:0= %#%^"^) do @set "iPartP=%%~a"%\n%
      for /F "tokens=* delims= " %%a in ^(^"%#%fPart:0= %#%^"^) do @set "fPartP=%%~a"%\n%
      %\n%
      if ^"%#%iPartP%#%%#%fPartP%#%^" == "" ^(%\n%
         ^>nul set /A "float=s"%\n%
      ^) else ^(%\n%
         if defined iPartP ^(%\n%
            set ^"iPartP=%#%iPartP: =0%#%^"%\n%
            set ^"fPartP=%#%fPart%#%^"%\n%
            set ^"string= %#%iPartP%#%^"%\n%
            set "op=+"%\n%
         ^) else if defined fPartP ^(%\n%
            set ^"fPartP=%#%fPartP: =0%#%^"%\n%
            for %%a in ^(%#%fPartP%#%^) do @set ^"string= %#%fPart:%%a=%#%^"%\n%
            set "op=-"%\n%
         ^)%\n%
         %\n%
         for %%a in ^(4096,2048,1024,512,256,128,64,32,16,8,4,2,1^) do @if not ^"%#%string:~%%a,1%#%^" == "" ^(%\n%
            set ^"string=%#%string:~%%a%#%^"%\n%
            ^>nul set /A ^"ePart%#%op%#%=%%a^"%\n%
         ^)%\n%
         %\n%
         set ^"significand=%#%iPartP%#%%#%fPartP%#%^"%\n%
         set "iPartP="%\n%
         set "fPartP="%\n%
%[%
::"   drop unneeded digits"^
::"   transform to: sPart * high_{8}.high_{7-0}low{7-0} * 5^ePart * 2^e_2"^
%]%
         set ^"significand=%#%significand:~0,17%#%0000000000000000^"%\n%
         set ^"high=%#%significand:~0,9%#%^"%\n%
         set ^"low=%#%significand:~9,8%#%^"%\n%
         ^>nul set /A "ePart-=1"%\n%
         ^>nul set /A "e_2=ePart"%\n%
%[%
::"         iterate on: 987654321; up to three times"^
%]%
         set "string= 8   4 2 "%\n%
         for %%a in ^(^"%#%high:~0,1%#%^"^) do @for %%b in ^(%#%string:~-%%~a%#%^) do @^(%\n%
            ^>nul set /A "c=(high&1)+1"%\n%
            set ^"low=%#%c%#%%#%low%#%^"%\n%
            ^>nul set /A "high>>=1", "low=(low>>1)-50000000", "e_2+=1"%\n%
            set ^"low=00000000%#%low%#%^"%\n%
            set ^"low=%#%low:~-8%#%^"%\n%
         ^)%\n%
         set "string="%\n%
         set "c="%\n%
%[%
::"   transform to: sPart * high_{8}.high_{7-0}low{7-0} * 2^e_2"^
%]%
         if %#%ePart%#% LSS 0 ^(%\n%
            for /L %%a in ^(%#%ePart%#%,1,-1^) do @^(%\n%
               ^>nul set /A ^"c=%#%high:~-1%#%%%5^"%\n%
               ^>nul set /A "cc=c+1"%\n%
               %\n%
               if %#%high%#% LSS 125000000 ^(%\n%
                  ^>nul set /A "high=(((high-c)/5)<<3)", "e_2-=3"%\n%
                  ^>nul set /A ^"low=^(^(%#%cc%#%%#%low%#%-100000000^)/5^)^<^<3^"%\n%
               ^) else ^(%\n%
                  ^>nul set /A "high=(((high-c)/5)<<2)", "e_2-=2"%\n%
                  ^>nul set /A ^"low=^(^(%#%cc%#%%#%low%#%-100000000^)/5^)^<^<2^"%\n%
               ^)%\n%
               %\n%
               if %#%low%#% GEQ 100000000 ^(%\n%
                  set ^"c=%#%low:~0,1%#%^"%\n%
                  set ^"low=%#%low:~1%#%^"%\n%
                  ^>nul set /A "high+=c"%\n%
               ^)%\n%
               %\n%
               set ^"low=00000000%#%low%#%^"%\n%
               set ^"low=%#%low:~-8%#%^"%\n%
            ^)%\n%
         ^) else if %#%ePart%#% GTR 0 ^(%\n%
            for /L %%a in ^(%#%ePart%#%,-1,1^) do @^(%\n%
               ^>nul set /A "c=high&7"%\n%
               ^>nul set /A "cc=c+1"%\n%
               %\n%
               if %#%high%#% LSS 160000000 ^(%\n%
                  ^>nul set /A ^"high=^(^(^(%#%high%#%-c^)^>^>2^)*5^)^", "e_2+=2"%\n%
                  ^>nul set /A ^"low=^(^(%#%cc%#%%#%low%#%-100000000^)^>^>2^)*5^"%\n%
               ^) else ^(%\n%
                  ^>nul set /A ^"high=^(^(^(%#%high%#%-c^)^>^>3^)*5^)^", "e_2+=3"%\n%
                  ^>nul set /A ^"low=^(^(%#%cc%#%%#%low%#%-100000000^)^>^>3^)*5^"%\n%
               ^)%\n%
               %\n%
               if %#%low%#% GEQ 100000000 ^(%\n%
                  set ^"c=%#%low:~0,1%#%^"%\n%
                  set ^"low=%#%low:~1%#%^"%\n%
                  ^>nul set /A "high+=c"%\n%
               ^)%\n%
               %\n%
               set ^"low=00000000%#%low%#%^"%\n%
               set ^"low=%#%low:~-8%#%^"%\n%
            ^)%\n%
         ^)%\n%
         set "ePart="%\n%
%[%
::"         compute fraction bits (f)"^
::"         setup maxIndex of bits to be computed: denormalized ones with e_2 <= 127;"^
::"         set e_2 to 127 although the exponent of denormalized float is 126 - coding."^
::"         maxIndex := 24+(127+!e_2!)-1 == 150+!e_2!"^
%]%
         if %#%e_2%#% LEQ -127 ^(%\n%
            ^>nul set /A "maxIndex=150+e_2"%\n%
            set "e_2=-127"%\n%
         ^) else if %#%e_2%#% GEQ 128 ^(%\n%
            set "maxIndex=-1"%\n%
         ^) else ^(%\n%
            set "maxIndex=24"%\n%
         ^)%\n%
         %\n%
         set "f=0"%\n%
         for /L %%a in ^(0, 1, %#%maxIndex%#%^) do @^(%\n%
            if ^"%#%high:~8%#%^" == "" ^(%\n%
               ^>nul set /A "f<<=1", "high<<=1", ^"low=^(1%#%low%#%-100000000^)^<^<1^"%\n%
            ^) else ^(%\n%
               ^>nul set /A "f=(f<<1)+1", "high=(high-100000000)<<1", ^"low=^(1%#%low%#%-100000000^)^<^<1^"%\n%
            ^)%\n%
            if NOT ^"%#%low:~8%#%^" == "" ^(%\n%
               ^>nul set /A "high+=1"%\n%
               set ^"low=00000000%#%low:~1%#%^"%\n%
            ^) else ^(%\n%
               set ^"low=00000000%#%low%#%^"%\n%
            ^)%\n%
            set ^"low=%#%low:~-8%#%^"%\n%
         ^)%\n%
%[%
::"   set up round bit (r) that specifies if rounding is performed, and"^
::"   if number is greater than the round bit (rUp: true==1 false==0); this means more bits or decimal digits are available"^
%]%
         ^>nul set /A "roundingMode+=0", "r=f&1", "f>>=1"%\n%
         %\n%
         if ^"%#%roundingMode%#%^" == "4" ^(%\n%
%[%
::"            No Rounding mode                                +2.5 +1.5 -1.5 -2.5"^
::"            4  toward -inf        [rounding down, or floor] +2.0 +1.0 -2.0 -3.0"^
%]%
            if NOT ^"%#%high%#%%#%low%#%^" == "000000000" set "r=1"%\n%
            if defined sPart ^>nul set /A "f+=r"%\n%
         ^) else if ^"%#%roundingMode%#%^" == "3" ^(%\n%
%[%
::"            No Rounding mode                                +2.5 +1.5 -1.5 -2.5"^
::"            3  toward +inf        [rounding up, or ceiling] +3.0 +2.0 -1.0 -2.0"^
%]%
            if NOT ^"%#%high%#%%#%low%#%^" == "000000000" set "r=1"%\n%
            if NOT defined sPart ^>nul set /A "f+=r"%\n%
         ^) else if ^"%#%roundingMode%#%^" == "2" ^(%\n%
%[%
::"            No Rounding mode                                +2.5 +1.5 -1.5 -2.5"^
::"            2  toward 0           [truncation, no rounding] +2.0 +1.0 -1.0 -2.0"^
%]%
            rem nothing left to do%\n%
         ^) else if ^"%#%roundingMode%#%^" == "1" ^(%\n%
%[%
::"            No Rounding mode                                +2.5 +1.5 -1.5 -2.5"^
::"            1  to nearest, ties away from zero              +3.0 +2.0 -2.0 -3.0"^
%]%
            ^>nul set /A "f+=r"%\n%
         ^) else ^(%\n%
%[%
::"            No Rounding mode                                +2.5 +1.5 -1.5 -2.5"^
::"            0  to nearest, ties to even           [default] +2.0 +2.0 -2.0 -2.0"^
%]%
            if %#%r%#% == 1 ^(%\n%
               if ^"%#%high%#%%#%low%#%^" == "000000000" ^(%\n%
                  ^>nul set /A "f+=(f&1)"%\n%
               ^) else ^(%\n%
                  ^>nul set /A "f+=1"%\n%
               ^)%\n%
            ^)%\n%
         ^)%\n%
%[%
::"         overflow checking"^
%]%
         if ^"%#%e_2%#%^" == "-127" ^(%\n%
            if ^"%#%f%#%^" == "8388608" ^>nul set /A "e_2+=1"%\n%
         ^) else if ^"%#%f%#%^" == "16777216" ^(%\n%
            ^>nul set /A "e_2+=1"%\n%
            ^>nul set /A "f>>=1"%\n%
         ^)%\n%
         %\n%
%[%
::"   build float"^
%]%
         ^>nul set /A "e=(e_2+127)<<23"%\n%
         if %#%e%#% == 255 ^( set "f=0" ^) else ^( ^>nul set /A "f&=0x007FFFFF" ^)%\n%
         ^>nul set /A "float=s|e|f"%\n%
      ^)%\n%
   ^)%\n%
   for %%a in ^(^"%#%float%#%^"^) do @for %%b in ^(^"%#%param[2]:~1%#%^"^) do @^(endlocal ^& ^(if "%%~b" == "" ^( echo %%~a^) else ^(set "%%~b=%%~a"^)^)^)%\n%
^) else setlocal enableDelayedExpansion ^& set params=, 

)
   (set #=)
::
:: end define $str2float


:: define $float2str
::   %~1 float value (int coding)
::   %~2 variable to store the resulting string if exists,
::       else echo string value if undefined
   ::
   ::      values for (simplified) rounding using table lookup:
   ::
   ::       float    | decimal value of f == 0x1                                       | precisition
   ::       (decstr) |                                                                 |
   ::      ----------+-----------------------------------------------------------------+-------------
   ::      ...       | ...                        ... ...                              | ...
   ::      ----------+-----------------------------------------------------------------+-------------
   ::       1        | 0,0000001 1920928955078125 /|\  1           2^-23=2^-13=2^-3    | 8
   ::       2        | 0,0000002 384185791015625   |   2                               | 8
   ::       4        | 0,0000004 76837158203125    |   5                               | 8   [7-8]
   ::       8        | 0,0000009 5367431640625     |  10 (hex: A)                      | 8-9 (7-8)
   ::                |                             |                                   |
   ::       16       |  0,000001 9073486328125     |   2                               | 8
   ::       32       |  0,000003 814697265625      |   4                               | 8
   ::       64       |  0,000007 62939453125       |   8                               | 8-9 (7-8)
   ::                |                             |                                   |
   ::       128      |   0,00001 52587890625       |   2                               | 8
   ::       256      |   0,00003 0517578125        |   3                               | 8
   ::       512      |   0,00006 103515625        \|/  6                               | 9
   ::      ----------+-----------------------------------------------------------------+-------------
   ::       1024     |    0,0001 220703125        /|\  1                               | 8
   ::       2048     |    0,0002 44140625          |   2                               | 8
   ::       4096     |    0,0004 8828125           |   5                               | 8   [7-8]
   ::       8192     |    0,0009 765625            |  10 (hex: A)                      | 8-9 (7-8)
   ::                |                             |                                   |
   ::       16384    |     0,001 953125            |   2                               | 8
   ::       32768    |     0,003 90625             |   4                               | 8
   ::       65536    |     0,007 8125              |   8                               | 9   (7-8)
   ::                |                             |                                   |
   ::       131072   |      0,01 5625              |   2                               | 8
   ::       262144   |      0,03 125               |   3                               | 8
   ::       524288   |      0,06 25               \|/  6                               | 9
   ::      ----------+-----------------------------------------------------------------+-------------
   ::       1048576  |       0,1 25               /|\  1                               | 8
   ::       2097152  |       0,2 5                 |   2                               | 8
   ::       4194304  |       0,5                   |   5                               | 8   [7-8]
   ::       ...      |  ...                       ... ...                              | ...
   ::      legend:
   ::       -  (x-y)  implemented (reduced precisition due to too big round delta value)
   ::       -  [x-y]  i've seen this in 'wild life', but i have no idea, why ...
   ::                 maybe because this table is imprecise; if this is true i won't fix it (higher precisition, so no problem)
   ::                        (i've also seen lower precisition on some denormalized numbers: i have no idea... if ... true... not fix it (...))
   ::
   ::      actually not needed: set "deltaR=125A248236"
   ::
   (set #=0)
   if "!#!" == "0" (set #=^^^^^^^^^^^^^^^!) else (set #=!)

   setlocal enableExtensions disableDelayedExpansion
   set LF=^


   set ^"\n=^^^%LF%%LF%^%LF%%LF%^<nul ^^^"
   set ^"[=%%~#^<nul ^^^%LF%%LF%^<nul ^^^"
   set ^"]=^<nul^^^%LF%%LF%^%LF%%LF%^<nul ^^^"
   endlocal & (


for %%# in ("") do set $float2str=@for %%N in ^(0 1^) do @if "%%~N" == "1" ^(%\n%
   %\n%
   set "N=0"%\n%
   set "param[1]= "%\n%
   set "param[2]= "%\n%
   for %%P in ^(%#%params%#%^) do @^(%\n%
      ^>nul set /A "N+=1"%\n%
      set ^"param[%#%N%#%]= %%~P^"%\n%
   ^)%\n%
   set "N="%\n%
   set "string="%\n%
%[%
::"   transform to: (s, e_2, f)"^
%]%
   set ^"float=%#%param[1]%#%^"%\n%
   ^>nul set /A "s=(float>>31)&1", "e_2=((float>>23)&0x000000FF)-127", "f=float&0x007FFFFF"%\n%
   if ^"%#%s%#%^" == "1" ^( set "sPart=-1" ^) else set "sPart=1"%\n%
   %\n%
   if ^"%#%e_2%#%^" == "128" ^(%\n%
      if ^"%#%f%#%^" == "0" ^(%\n%
         set ^"string=%#%sPart:1=%#%inf^"%\n%
      ^) else if ^"%#%f%#%^" == "8388607" ^(%\n%
         set ^"string=%#%sPart:1=%#%NaN^"%\n%
      ^) else ^(%\n%
         ^>nul set /A ^"f=f^|0x00800000^"%\n%
         set "hexDigits=0123456789ABCDEF"%\n%
         set "value="%\n%
         set "string="%\n%
         for /L %%a in ^(1,1,6^) do @^(%\n%
            ^>nul set /A "value=f&0xF", "f>>=4"%\n%
            for %%b in ^(^"%#%value%#%^"^) do @set ^"string=%#%hexDigits:~%%~b,1%#%%#%string%#%^"%\n%
         ^)%\n%
         set ^"string=%#%sPart:1=%#%NaN^(7F%#%string%#%^)^"%\n%
      ^)%\n%
   ^) else if ^"%#%e_2%#%,%#%f%#%^" == "-127,0" ^(%\n%
      set ^"string=%#%sPart:~0,-1%#%0.0^"%\n%
   ^) else ^(%\n%
%[%
::"      transform to: sPart * high_{8}(==1).high_{7-0}low{7-0} * 2^e"^
%]%
      if ^"%#%e_2%#%^" == "-127" ^(%\n%
         for /L %%a in ^(0,1,23^) do @if %#%f%#% LSS 8388608 ^>nul set /A "e_2-=1", "f<<=1"%\n%
         set ^>nul /A "e_2+=1"%\n%
      ^) else set ^>nul /A "f|=0x00800000"%\n%
      %\n%
      set "high=0"%\n%
      set "low=00000000"%\n%
      for /L %%a in ^(0, 1, 23^) do @^(%\n%
         ^>nul set /A "b=f&1", "f>>=1", "c=(high&1)+1"%\n%
         set ^"d=%#%low:~0,1%#%^"%\n%
         ^>nul set /A ^"low=^(%#%c%#%%#%low%#%-100000000^)^>^>1^"%\n%
         set ^"low=00000000%#%low%#%^"%\n%
         set ^"low=%#%low:~-8%#%^"%\n%
         ^>nul set /A ^"high=^(high^>^>1^)+%#%b%#%00000000^"%\n%
      ^)%\n%
%[%
::"      transform to: sPart * 0.high_{7-0}low{7-0} * 10^ePart"^
%]%
      set "ePart=0"%\n%
      if %#%e_2%#% GTR 0 ^(%\n%
         ^>nul set /A "N=(e_2>>1)+1"%\n%
         for /L %%a in ^(%#%N%#%,-1,1^) do @^(%\n%
            if %#%e_2%#% GTR %#%ePart%#% ^(%\n%
               ^>nul set /A ^"c=^(%#%high:~-1%#%%%5^)+1^", ^"cc=%#%low:~-1%#%%%5^"%\n%
               if %#%high%#% LSS 125000000 ^(%\n%
                  ^>nul set /A "high=(high/5)<<3", "e_2-=3", "ePart+=1", ^"low=^(^(^(%#%c%#%%#%low%#%-100000000^)/5^)^<^<3^)+^(^(cc^<^<3^)/5^)^"%\n%
               ^) else ^(%\n%
                  ^>nul set /A "high=(high/5)<<2", "e_2-=2", "ePart+=1", ^"low=^(^(^(%#%c%#%%#%low%#%-100000000^)/5^)^<^<2^)+^(^(cc^<^<2^)/5^)^"%\n%
               ^)%\n%
               if %#%low%#% GEQ 100000000 ^(%\n%
                  ^>nul set /A ^"high+=%#%low:~0,1%#%^"%\n%
                  set ^"low=00000000%#%low:~1%#%^"%\n%
               ^) else ^(%\n%
                  set ^"low=00000000%#%low%#%^"%\n%
               ^)%\n%
               set ^"low=%#%low:~-8%#%^"%\n%
            ^)%\n%
         ^)%\n%
         %\n%
         ^>nul set /A "e_2-=ePart"%\n%
         if %#%e_2%#% LSS 0 ^(%\n%
            ^>nul set /A ^"cc=^(%#%high:~-1%#%^&^(^(1^<^<^(-e_2^)^)-1^)^)+1^"%\n%
            ^>nul set /A "high>>=(-e_2)", ^"low=^(^(%#%cc%#%%#%low%#%-100000000^)^>^>^(-e_2^)^)^"%\n%
            set ^"low=00000000%#%low%#%^"%\n%
            set ^"low=%#%low:~-8%#%^"%\n%
            set "e_2=0"%\n%
         ^) else ^(%\n%
            set ^"low=%#%high:~-1%#%%#%low%#%^"%\n%
            set ^"low=%#%low:~0,8%#%^"%\n%
            set ^"high=%#%high:~0,-1%#%^"%\n%
            if not defined high set "high=0"%\n%
            ^>nul set /A "ePart+=1"%\n%
         ^)%\n%
      ^) else if %#%e_2%#% LSS 0 ^(%\n%
         ^>nul set /A "N=(e_2>>1)-1", "ePart-=3"%\n%
         for /L %%a in ^(%#%N%#%,1,-1^) do @^(%\n%
            if %#%e_2%#% LSS %#%ePart%#% ^(%\n%
               if %#%high%#% LSS 160000000 ^(%\n%
                  ^>nul set /A "c=(high&3)+1"%\n%
                  ^>nul set /A ^"cLow=%#%c%#%%#%low%#%-100000000^", "high=((high>>2)*5)", "e_2+=2", "ePart-=1", "low=((cLow>>2)*5)+(((cLow&2)*5)>>2)"%\n%
               ^) else ^(%\n%
                  ^>nul set /A "c=(high&7)+1"%\n%
                  ^>nul set /A ^"cLow=%#%c%#%%#%low%#%-100000000^", "high=((high>>3)*5)", "e_2+=3", "ePart-=1", "low=((cLow>>3)*5)+(((cLow&3)*5)>>3)"%\n%
               ^)%\n%
               if %#%low%#% GEQ 100000000 ^(%\n%
                  ^>nul set /A ^"high+=%#%low:~0,1%#%^"%\n%
                  set ^"low=00000000%#%low:~1%#%^"%\n%
               ^) else set ^"low=00000000%#%low%#%^"%\n%
               set ^"low=%#%low:~-8%#%^"%\n%
            ^)%\n%
         ^)%\n%
         %\n%
         ^>nul set /A "e_2-=(ePart+=3)"%\n%
         if %#%e_2%#% LSS 0 ^(%\n%
            ^>nul set /A ^"cc=^(%#%high:~-1%#%^&^(^(1^<^<^(-e_2^)^)-1^)^)+1^"%\n%
            ^>nul set /A "high>>=(-e_2)", ^"low=^(^(%#%cc%#%%#%low%#%-100000000^)^>^>^(-e_2^)^)^"%\n%
            set ^"low=00000000%#%low%#%^"%\n%
            set ^"low=%#%low:~-8%#%^"%\n%
            set "e_2=0"%\n%
         ^) else ^(%\n%
            set ^"low=%#%high:~-1%#%%#%low%#%^"%\n%
            set ^"low=%#%low:~0,8%#%^"%\n%
            set ^"high=%#%high:~0,-1%#%^"%\n%
            ^>nul set /A "ePart+=1"%\n%
         ^)%\n%
      ^) else (%\n%
         set ^"low=%#%high:~-1%#%%#%low%#%^"%\n%
         set ^"low=%#%low:~0,8%#%^"%\n%
         set ^"high=%#%high:~0,-1%#%^"%\n%
         ^>nul set /A "ePart+=1"%\n%
      ^)%\n%
%[%
::"   perform rounding: see table above"^
::"      initial values are upper bounds only"^
%]%
      set "precisition=8889889889"%\n%
      ^>nul set /A "rounding+=0", "eR=(((float>>23)&0x000000FF)-127)+1000"%\n%
      if %#%eR%#% EQU 873 ^>nul set /A "eR=874"%\n%
      for %%a in ^(^"%#%er:~-1%#%^"^) do @^(%\n%
         ^>nul set /A ^"precisition=%#%precisition:~%%~a,1%#%^"%\n%
         if ^"%#%precisition%#%^" == "9" ^(%\n%
            if NOT ^"%#%high:~0,1%#%^" == "1" ^(%\n%
               set "precisition=8"%\n%
            ^)%\n%
         ^)%\n%
         if "%%~a" == "3" ^>nul set /A "precisition-=1"%\n%
         if "%%~a" == "6" ^>nul set /A "precisition-=1"%\n%
      ^)%\n%
%[%
::"      REM #1234567890   "^
::"      REM i0123456789   "^
::"      REM  xxxxxxlr---  "^
::"      REM  xxxxxxxlr--- "^
::"      REM  xxxxxxxxlr---"^
%]%
      set ^"rest=%#%high%#%%#%low%#%^"%\n%
      if ^"%#%precisition%#%^" == "7" ^(%\n%
         set ^"high=%#%rest:~0,6%#%^"%\n%
         set  ^"low=%#%rest:~6,2%#%^"%\n%
         set ^"rest=%#%rest:~8%#%^"%\n%
      ^) else if ^"%#%precisition%#%^" == "8" ^(%\n%
         set ^"high=%#%rest:~0,7%#%^"%\n%
         set  ^"low=%#%rest:~7,2%#%^"%\n%
         set ^"rest=%#%rest:~9%#%^"%\n%
      ^) else ^(%\n%
         set ^"high=%#%rest:~0,8%#%^"%\n%
         set  ^"low=%#%rest:~8,2%#%^"%\n%
         set ^"rest=%#%rest:~10%#%^"%\n%
      ^)%\n%
      %\n%
      if ^"%#%roundingMode%#%^" == "4" ^(%\n%
%[%
::"         No Rounding mode                                +2.5 +1.5 -1.5 -2.5"^
::"         4  toward -inf        [rounding down, or floor] +2.0 +1.0 -2.0 -3.0"^
%]%
         if ^"%#%sPart%#%^" == "-1" ^(%\n%
            for /F "delims=0" %%a in ^(^"%#%low:~1%#%%#%rest%#%#^"^) do @^(%\n%
               if "%%~a" == "#" ^( set ^"low=%#%low:~0,1%#%^"%\n%
               ^) else ^>nul set /A ^"low=%#%low:~0,1%#%+1^"%\n%
            ^)%\n%
         ^) else set ^"low=%#%low:~0,1%#%^"%\n%
      ^) else if ^"%#%roundingMode%#%^" == "3" ^(%\n%
%[%
::"         No Rounding mode                                +2.5 +1.5 -1.5 -2.5"^
::"         3  toward +inf        [rounding up, or ceiling] +3.0 +2.0 -1.0 -2.0"^
%]%
         if ^"%#%sPart%#%^" == "1" ^(%\n%
            for /F "delims=0" %%a in ^(^"%#%low:~1%#%%#%rest%#%#^"^) do @^(%\n%
               if "%%~a" == "#" ^( set ^"low=%#%low:~0,1%#%^"%\n%
               ^) else ^>nul set /A ^"low=%#%low:~0,1%#%+1^"%\n%
            ^)%\n%
         ^) else set ^"low=%#%low:~0,1%#%^"%\n%
      ^) else if ^"%#%roundingMode%#%^" == "2" ^(%\n%
%[%
::"         No Rounding mode                                +2.5 +1.5 -1.5 -2.5"^
::"         2  toward 0           [truncation, no rounding] +2.0 +1.0 -1.0 -2.0"^
%]%
         rem nothing left to do%\n%
      ^) else if ^"%#%roundingMode%#%^" == "1" ^(%\n%
%[%
::"         No Rounding mode                                +2.5 +1.5 -1.5 -2.5"^
::"         1  to nearest, ties away from zero              +3.0 +2.0 -2.0 -3.0"^
%]%
         if %#%low:~1%#% GEQ 5 ^( ^>nul set /A ^"low=%#%low:~0,1%#%+1^"%\n%
         ^) else set ^"low=%#%low:~0,1%#%^"%\n%
      ^) else ^(%\n%
%[%
::"         No Rounding mode                                +2.5 +1.5 -1.5 -2.5"^
::"         0  to nearest, ties to even           [default] +2.0 +2.0 -2.0 -2.0"^
%]%
         for /F "delims=02468" %%a in ^(^"%#%low:~0,1%#%#^"^) do @for /F "delims=0" %%b in ^(^"%#%rest%#%#^"^) do @^(%\n%
            if "%%~a%%~b" == "##" ^( set ^"low=%#%low%#%0^"%\n%
            ^) else set ^"low=%#%low%#%1^"%\n%
         ^)%\n%
         if %#%low:~1%#% GTR 50 ^( ^>nul set /A ^"low=%#%low:~0,1%#%+1^"%\n%
         ^) else set ^"low=%#%low:~0,1%#%^"%\n%
      ^)%\n%
%[%
::"      check overflow"^
%]%
      if %#%low%#% GEQ 10 ^>nul set /A ^"low=%#%low:~1%#%^", "high+=1"%\n%
%[%
::"      transform to: sPart * high.low * 10^ePart, digits := #|high.low|"^
%]%
      set ^"low=%#%high%#%%#%low%#%^"%\n%
      set ^"digits=%#%precisition%#%^"%\n%
      for %%a in ^(^"%#%precisition%#%^"^) do @if NOT ^"%#%low:~%%~a%#%^" == "" ^(%\n%
         ^>nul set /A "ePart+=1"%\n%
         ^>nul set /A "digits+=1"%\n%
      ^)%\n%
%[%
::"      transform to: nice numbers"^
::"      no leading zero (except the following explicitely allow this)"^
%]%
      set ^"high=%#%low:~0,1%#%^"%\n%
      set ^"low=%#%low:~1%#%^"%\n%
      ^>nul set /A "ePart-=1"%\n%
%[%
::"      use form without exponent if possible (max 7 integer / -3 fraction digits are allowed)"^
%]%
      for %%a in ^(^"%#%ePart%#%^"^) do @^(%\n%
         if 1 LEQ %%~a if %%~a LSS 7 ^(%\n%
            set ^"high=%#%high%#%%#%low:~0,%%~a%#%^"%\n%
            set ^"low=%#%low:~%%~a%#%^"%\n%
            ^>nul set /A "ePart-=%%~a"%\n%
         ^)%\n%
         if -3 LEQ %%~a if %%~a LEQ -1 ^(%\n%
            set "zeroes=000000000"%\n%
            for %%b in ^(^"%#%ePart%#%^"^) do @if ^"%#%low:~%%~b%#%^" == ^"%#%zeroes:~%%~b%#%^" ^(%\n%
               set ^"high=000000000%#%high%#%^"%\n%
               set ^"low=%#%high:~%%~a%#%%#%low%#%^"%\n%
               set "high="%\n%
               ^>nul set /A "ePart-=%%~a"%\n%
            ^)%\n%
         ^)%\n%
      ^)%\n%
%[%
::"      no trailing zeroes"^
%]%
      for /L %%a in ^(1,1,%#%digits%#%^) do @if ^"%#%low:~-1%#%^" == "0" set ^"low=%#%low:~0,-1%#%^"%\n%
%[%
::"      avoid lonely separator"^
%]%
      if NOT defined high set "high=0"%\n%
      if NOT defined low set "low=0"%\n%
%[%
::"   create float string"^
%]%
      ^>nul set /A "ePart+=0"%\n%
      set ^"string=%#%sPart:~0,-1%#%%#%high%#%.%#%low%#%^"%\n%
      if not ^"%#%ePart%#%^" == "0" set ^"string=%#%string%#% e%#%ePart%#%^"%\n%
   ^)%\n%
   for %%a in ^(^"%#%string%#%^"^) do @for %%b in ^(^"%#%param[2]:~1%#%^"^) do @^(endlocal ^& ^(if "%%~b" == "" ^(echo^(%%~a^) else ^(set "%%~b=%%~a"^)^)^)%\n%
^) else setlocal enableDelayedExpansion ^& set params=, 

)
   (set #=)
::
:: end define $float2str


:: define $floatAdd
::   %~1 summand1 float in int coding
::   %~2 summand2 float in int coding
::   %~3 resulting float in int coding
   (set #=0)
   if "!#!" == "0" (set bOR=^^^^) else (set bOR=^^)
   if "!#!" == "0" (set #=^^^^^^^^^^^^^^^!) else (set #=!)

   setlocal enableExtensions disableDelayedExpansion
   set LF=^


   set ^"\n=^^^%LF%%LF%^%LF%%LF%^<nul ^^^"
   set ^"[=%%~#^<nul ^^^%LF%%LF%^<nul ^^^"
   set ^"]=^<nul^^^%LF%%LF%^%LF%%LF%^<nul ^^^"
   endlocal & (

for %%# in ("") do set $floatAdd=@for %%N in ^(0 1^) do @if %%~N == 1 ^(%\n%
   set "N=0"%\n%
   set "param[1]= "%\n%
   set "param[2]= "%\n%
   set "param[3]= "%\n%
   for %%P in ^(%#%params%#%^) do @^(%\n%
      ^>nul set /A "N+=1"%\n%
      set ^"param[%#%N%#%]= %%~P^"%\n%
   ^)%\n%
   set "N="%\n%
   set "result="%\n%
   ^>nul set /A "float1=param[1]", "float2=param[2]"%\n%
   ^>nul set /A "s1=(float1>>31)&1", "e1=((float1>>23)&0x000000FF)-127", "f1=float1&0x007FFFFF"%\n%
   ^>nul set /A "s2=(float2>>31)&1", "e2=((float2>>23)&0x000000FF)-127", "f2=float2&0x007FFFFF"%\n%
   ^>nul set /A "deltaE=(e1-e2)"%\n%
   if %#%deltaE%#% LSS 0 ^>nul set /A "deltaE=-deltaE"%\n%
   %\n%
   if ^"%#%e1%#%^" == "128" ^(%\n%
      if NOT ^"%#%e2%#%^" == "128" ^(%\n%
         ^>nul set /A "result=float1"%\n%
      ^) else if ^"%#%s1%#%^" == ^"%#%s2%#%^" ^(%\n%
         ^>nul set /A "result=float1|float2"%\n%
      ^) else ^(%\n%
         ^>nul set /A "result=0x7FFFFFFF"%\n%
      ^)%\n%
   ^) else if %#%e2%#% == 128 ^(%\n%
      ^>nul set /A "result=float2"%\n%
   ^) else if %#%deltaE%#% GEQ 25 ^(%\n%
      if %#%e1%#% LSS %#%e2%#% ^(%\n%
         ^>nul set /A "result=float1"%\n%
      ^) else ^(%\n%
         ^>nul set /A "result=float2"%\n%
      ^)%\n%
   ^) else ^(%\n%
      if %#%e1%#% == -127 ^( ^>nul set /A "e1+=1" ^) else ^( ^>nul set /A "f1|=0x00800000" ^)%\n%
      if %#%e2%#% == -127 ^( ^>nul set /A "e2+=1" ^) else ^( ^>nul set /A "f2|=0x00800000" ^)%\n%
%[%
::"   watch one more bit needed to round (<= 25 bits)"^
%]%
      ^>nul set /A "e1-=1", "f1<<=1", "e2-=1", "f2<<=1"%\n%
      ^>nul set /A "r=0", "rUp=0"%\n%
      ^>nul set /A "rest=0x01FFFFFF%bOR%((0x01FFFFFF>>deltaE)<<deltaE)"%\n%
      %\n%
      if %#%e1%#% LSS %#%e2%#% ^( ^>nul set /A "e1+=deltaE", "rest&=f1", "f1>>=(deltaE)"%\n%
      ^) else                     ^>nul set /A "e2+=deltaE", "rest&=f2", "f2>>=(deltaE)"%\n%
      %\n%
      if ^"%#%s1%#%^" == ^"%#%s2%#%^" ^(%\n%
         ^>nul set /A "sR=s1", "eR=e1", "fR=f1+f2"%\n%
      ^) else ^(%\n%
         if %#%s1%#% == 1 set ^"f1=-%#%f1%#%^"%\n%
         if %#%s2%#% == 1 set ^"f2=-%#%f2%#%^"%\n%
         ^>nul set /A "sR=0", "eR=e1", "fR=f1+f2"%\n%
         if ^"%#%fR:~0,1%#%^" == "-" ^>nul set /A "sR=1", "fR=-fR"%\n%
      ^)%\n%
      %\n%
      ^>nul set /A "deltaE=eR+126"%\n%
      if %#%deltaE%#% LSS 0 ^( ^>nul set /A "deltaE=0"%\n%
      ^) else if %#%deltaE%#% GTR 25 ^>nul set /A "deltaE=25"%\n%
      for /L %%a in ^(1,1,%#%deltaE%#%^) do @if %#%fR%#% LSS 16777216 ^>nul set /A "fR<<=1", "eR-=1"%\n%
%[%
::"   perform rounding (renormalize to 24 bits again)"^
%]%
      ^>nul set /A "roundingMode+=0", "r=fR&1", "fR>>=1", "eR+=1"%\n%
      if 0x1000000 LEQ %#%fR%#% ^>nul set /A "fR>>=1", "eR+=1"%\n%
      %\n%
      if ^"%#%roundingMode%#%^" == "4" ^(%\n%
%[%
::"         No Rounding mode                                +2.5 +1.5 -1.5 -2.5"^
::"         4  toward -inf        [rounding down, or floor] +2.0 +1.0 -2.0 -3.0"^
%]%
         if NOT ^"%#%rest%#%^" == "0" set "r=1"%\n%
         if ^"%#%sR%#%^" == "1" ^>nul set /A "fR+=r"%\n%
      ^) else if ^"%#%roundingMode%#%^" == "3" ^(%\n%
%[%
::"         No Rounding mode                                +2.5 +1.5 -1.5 -2.5"^
::"         3  toward +inf        [rounding up, or ceiling] +3.0 +2.0 -1.0 -2.0"^
%]%
         if NOT ^"%#%rest%#%^" == "0" set "r=1"%\n%
         if ^"%#%sR%#%^" == "0" ^>nul set /A "fR+=r"%\n%
      ^) else if ^"%#%roundingMode%#%^" == "2" ^(%\n%
%[%
::"         No Rounding mode                                +2.5 +1.5 -1.5 -2.5"^
::"         2  toward 0           [truncation, no rounding] +2.0 +1.0 -1.0 -2.0"^
%]%
         rem nothing left to do%\n%
      ^) else if ^"%#%roundingMode%#%^" == "1" (%\n%
%[%
::"         No Rounding mode                                +2.5 +1.5 -1.5 -2.5"^
::"         1  to nearest, ties away from zero              +3.0 +2.0 -2.0 -3.0"^
%]%
         ^>nul set /A "fR+=r"%\n%
      ^) else ^(%\n%
%[%
::"         No Rounding mode                                +2.5 +1.5 -1.5 -2.5"^
::"         0  to nearest, ties to even           [default] +2.0 +2.0 -2.0 -2.0"^
%]%
         if %#%r%#% == 1 ^(%\n%
            if ^"%#%rest%#%^" == "0" ^(%\n%
               ^>nul set /A "fR+=(fR&1)"%\n%
            ^) else ^(%\n%
               ^>nul set /A "fR+=1"%\n%
            ^)%\n%
         ^)%\n%
      ^)%\n%
%[%
::"      overflow checking"^
%]%
      if 0x1000000 LEQ %#%fR%#% ^>nul set /A "fR>>=1", "eR+=1"%\n%
      %\n%
      if %#%fR%#% LSS 8388608 ^( ^>nul set /A "result=((sR&1)<<31)|fR"%\n%
      ^) else ^>nul set /A "result=((sR&1)<<31)|((eR+127)<<23)|(fR&0x7FFFFF)"%\n%
   ^)%\n%
   for %%a in ^(^"%#%result%#%^"^) do @for %%b in ^(^"%#%param[3]:~1%#%^"^) do @^(endlocal ^& ^(if "%%~b" == "" ^( echo %%~a^) else ^(set "%%~b=%%~a"^)^)^)%\n%
^) else setlocal enableDelayedExpansion ^& set params=, 
)
   (set #=)
::
:: end define $floatAdd


:: define $floatSub
::   %~1 summand1 float in int coding
::   %~2 summand2 float in int coding
::   %~3 resulting float in int coding
   (set #=0)
   if "!#!" == "0" (set bOR=^^^^) else (set bOR=^^)
   if "!#!" == "0" (set #=^^^^^^^^^^^^^^^!) else (set #=!)

   setlocal enableExtensions disableDelayedExpansion
   set LF=^


   set ^"\n=^^^%LF%%LF%^%LF%%LF%^<nul ^^^"
   set ^"[=%%~#^<nul ^^^%LF%%LF%^<nul ^^^"
   set ^"]=^<nul^^^%LF%%LF%^%LF%%LF%^<nul ^^^"
   endlocal & (

for %%# in ("") do set $floatSub=@for %%N in ^(0 1^) do @if %%~N == 1 ^(%\n%
   set "N=0"%\n%
   set "param[1]= "%\n%
   set "param[2]= "%\n%
   set "param[3]= "%\n%
   for %%P in ^(%#%params%#%^) do @^(%\n%
      ^>nul set /A "N+=1"%\n%
      set ^"param[%#%N%#%]= %%~P^"%\n%
   ^)%\n%
   set "N="%\n%
   set "result="%\n%
   ^>nul set /A "float1=param[1]", "float2=param[2]"%\n%
   ^>nul set /A "s1=(float1>>31)&1", "e1=((float1>>23)&0x000000FF)-127", "f1=float1&0x007FFFFF"%\n%
   ^>nul set /A "s2=(float2>>31)&1", "e2=((float2>>23)&0x000000FF)-127", "f2=float2&0x007FFFFF"%\n%
   ^>nul set /A "s2=(1-s2)"%\n%
   ^>nul set /A "deltaE=(e1-e2)"%\n%
   if %#%deltaE%#% LSS 0 ^>nul set /A "deltaE=-deltaE"%\n%
   %\n%
   if ^"%#%e1%#%^" == "128" ^(%\n%
      if NOT ^"%#%e2%#%^" == "128" ^(%\n%
         ^>nul set /A "result=float1"%\n%
      ^) else if ^"%#%s1%#%^" == ^"%#%s2%#%^" ^(%\n%
         ^>nul set /A "result=float1|float2"%\n%
      ^) else ^(%\n%
         ^>nul set /A "result=0x7FFFFFFF"%\n%
      ^)%\n%
   ^) else if %#%e2%#% == 128 ^(%\n%
      ^>nul set /A "result=float2"%\n%
   ^) else if %#%deltaE%#% GEQ 25 ^(%\n%
      if %#%e1%#% LSS %#%e2%#% ^(%\n%
         ^>nul set /A "result=float1"%\n%
      ^) else ^(%\n%
         ^>nul set /A "result=float2"%\n%
      ^)%\n%
   ^) else ^(%\n%
      if %#%e1%#% == -127 ^( ^>nul set /A "e1+=1" ^) else ^( ^>nul set /A "f1|=0x00800000" ^)%\n%
      if %#%e2%#% == -127 ^( ^>nul set /A "e2+=1" ^) else ^( ^>nul set /A "f2|=0x00800000" ^)%\n%
%[%
::"   watch one more bit needed to round (<= 25 bits)"^
%]%
      ^>nul set /A "e1-=1", "f1<<=1", "e2-=1", "f2<<=1"%\n%
      ^>nul set /A "r=0", "rUp=0"%\n%
      ^>nul set /A "rest=0x01FFFFFF%bOR%((0x01FFFFFF>>deltaE)<<deltaE)"%\n%
      %\n%
      if %#%e1%#% LSS %#%e2%#% ^( ^>nul set /A "e1+=deltaE", "rest&=f1", "f1>>=(deltaE)"%\n%
      ^) else                     ^>nul set /A "e2+=deltaE", "rest&=f2", "f2>>=(deltaE)"%\n%
      %\n%
      if ^"%#%s1%#%^" == ^"%#%s2%#%^" ^(%\n%
         ^>nul set /A "sR=s1", "eR=e1", "fR=f1+f2"%\n%
      ^) else ^(%\n%
         if %#%s1%#% == 1 set ^"f1=-%#%f1%#%^"%\n%
         if %#%s2%#% == 1 set ^"f2=-%#%f2%#%^"%\n%
         ^>nul set /A "sR=0", "eR=e1", "fR=f1+f2"%\n%
         if ^"%#%fR:~0,1%#%^" == "-" ^>nul set /A "sR=1", "fR=-fR"%\n%
      ^)%\n%
      %\n%
      ^>nul set /A "deltaE=eR+126"%\n%
      if %#%deltaE%#% LSS 0 ^( ^>nul set /A "deltaE=0"%\n%
      ^) else if %#%deltaE%#% GTR 25 ^>nul set /A "deltaE=25"%\n%
      for /L %%a in ^(1,1,%#%deltaE%#%^) do @if %#%fR%#% LSS 16777216 ^>nul set /A "fR<<=1", "eR-=1"%\n%
%[%
::"   perform rounding (renormalize to 24 bits again)"^
%]%
      ^>nul set /A "roundingMode+=0", "r=fR&1", "fR>>=1", "eR+=1"%\n%
      if 0x1000000 LEQ %#%fR%#% ^>nul set /A "fR>>=1", "eR+=1"%\n%
      %\n%
      if ^"%#%roundingMode%#%^" == "4" ^(%\n%
%[%
::"         No Rounding mode                                +2.5 +1.5 -1.5 -2.5"^
::"         4  toward -inf        [rounding down, or floor] +2.0 +1.0 -2.0 -3.0"^
%]%
         if NOT ^"%#%rest%#%^" == "0" set "r=1"%\n%
         if ^"%#%sR%#%^" == "1" ^>nul set /A "fR+=r"%\n%
      ^) else if ^"%#%roundingMode%#%^" == "3" ^(%\n%
%[%
::"         No Rounding mode                                +2.5 +1.5 -1.5 -2.5"^
::"         3  toward +inf        [rounding up, or ceiling] +3.0 +2.0 -1.0 -2.0"^
%]%
         if NOT ^"%#%rest%#%^" == "0" set "r=1"%\n%
         if ^"%#%sR%#%^" == "0" ^>nul set /A "fR+=r"%\n%
      ^) else if ^"%#%roundingMode%#%^" == "2" ^(%\n%
%[%
::"         No Rounding mode                                +2.5 +1.5 -1.5 -2.5"^
::"         2  toward 0           [truncation, no rounding] +2.0 +1.0 -1.0 -2.0"^
%]%
         rem nothing left to do%\n%
      ^) else if ^"%#%roundingMode%#%^" == "1" (%\n%
%[%
::"         No Rounding mode                                +2.5 +1.5 -1.5 -2.5"^
::"         1  to nearest, ties away from zero              +3.0 +2.0 -2.0 -3.0"^
%]%
         ^>nul set /A "fR+=r"%\n%
      ^) else ^(%\n%
%[%
::"         No Rounding mode                                +2.5 +1.5 -1.5 -2.5"^
::"         0  to nearest, ties to even           [default] +2.0 +2.0 -2.0 -2.0"^
%]%
         if %#%r%#% == 1 ^(%\n%
            if ^"%#%rest%#%^" == "0" ^(%\n%
               ^>nul set /A "fR+=(fR&1)"%\n%
            ^) else ^(%\n%
               ^>nul set /A "fR+=1"%\n%
            ^)%\n%
         ^)%\n%
      ^)%\n%
%[%
::"      overflow checking"^
%]%
      if 0x1000000 LEQ %#%fR%#% ^>nul set /A "fR>>=1", "eR+=1"%\n%
      %\n%
      if %#%fR%#% LSS 8388608 ^( ^>nul set /A "result=((sR&1)<<31)|fR"%\n%
      ^) else ^>nul set /A "result=((sR&1)<<31)|((eR+127)<<23)|(fR&0x7FFFFF)"%\n%
   ^)%\n%
   for %%a in ^(^"%#%result%#%^"^) do @for %%b in ^(^"%#%param[3]:~1%#%^"^) do @^(endlocal ^& ^(if "%%~b" == "" ^( echo %%~a^) else ^(set "%%~b=%%~a"^)^)^)%\n%
^) else setlocal enableDelayedExpansion ^& set params=, 
)
   (set #=)
::
:: end define $floatSub


:: define $floatMul
::   %~1 multiplicand1 float in int coding
::   %~2 multiplicand1 float in int coding
::   %~3 resulting float in int coding
::
:: (a1 * 2^12 + a0) * (b1 * 2^12 + b0) == a1*b1*2^24 + (a1*b0 + a0*b1)*2^12 + a0*b0
:: 1...<n>...1 * 1...<n>...1 == 1...<n-1>...1 0...<n-1>...0 1
:: => |ax*by|==2*12==24
:: let be:
::   a1*b1 = AAAAAAAAAAAAAAAAAAAAAAAA,
::   a1*b0 = BBBBBBBBBBBBCCCCCCCCCCCC,
::   a0*b1 = DDDDDDDDDDDDEEEEEEEEEEEE,
::   a0*b0 = FFFFFFFFFFFFFFFFFFFFFFFF
:: f1 * f2 == AAAAAAAAAAAAAAAAAAAAAAAA000000000000000000000000 +
::                        BBBBBBBBBBBBCCCCCCCCCCCC000000000000 +
::                        DDDDDDDDDDDDEEEEEEEEEEEE000000000000 +
::                                    FFFFFFFFFFFFFFFFFFFFFFFF
   (set #=0)
   if "!#!" == "0" (set bOR=^^^^) else (set bOR=^^)
   if "!#!" == "0" (set #=^^^^^^^^^^^^^^^!) else (set #=!)

   setlocal enableExtensions disableDelayedExpansion
   set LF=^


   set ^"\n=^^^%LF%%LF%^%LF%%LF%^<nul ^^^"
   set ^"[=%%~#^<nul ^^^%LF%%LF%^<nul ^^^"
   set ^"]=^<nul^^^%LF%%LF%^%LF%%LF%^<nul ^^^"
   endlocal & (

for %%# in ("") do set $floatMul=@for %%N in ^(0 1^) do @if %%~N == 1 ^(%\n%
   set "N=0"%\n%
   set "param[1]= "%\n%
   set "param[2]= "%\n%
   set "param[3]= "%\n%
   for %%P in ^(%#%params%#%^) do @^(%\n%
      ^>nul set /A "N+=1"%\n%
      set ^"param[%#%N%#%]= %%~P^"%\n%
   ^)%\n%
   set "N="%\n%
   set "result="%\n%
   ^>nul set /A "float1=param[1]", "float2=param[2]"%\n%
   ^>nul set /A "s1=(float1>>31)&1", "e1=((float1>>23)&0x000000FF)-127", "f1=float1&0x007FFFFF"%\n%
   ^>nul set /A "s2=(float2>>31)&1", "e2=((float2>>23)&0x000000FF)-127", "f2=float2&0x007FFFFF"%\n%
   %\n%
   if ^"%#%e1%#%^" == "128" ^(%\n%
      if NOT ^"%#%e2%#%^" == "128" ^(%\n%
         ^>nul set /A "result=((s1%bOR%s2)<<31)|((e1+127)<<23)|f1"%\n%
      ^) else if ^"%#%f1%#%^" == ^"%#%f2%#%^" ^(%\n%
         ^>nul set /A "result=((s1%bOR%s2)<<31)|((e1+127)<<23)|f1"%\n%
      ^) else ^(%\n%
         ^>nul set /A "result=((s1%bOR%s2)<<31)|0x7FFFFFFF"%\n%
      ^)%\n%
   ^) else if ^"%#%e2%#%^" == "128" ^(%\n%
      ^>nul set /A "result=((s1%bOR%s2)<<31)|((e2+127)<<23)|f2"%\n%
   ^) else ^(%\n%
      if ^"%#%e1%#%^" == "-127" ^( ^>nul set /A "e1+=1" ^) else ^>nul set /A "f1|=0x00800000"%\n%
      if ^"%#%e2%#%^" == "-127" ^( ^>nul set /A "e2+=1" ^) else ^>nul set /A "f2|=0x00800000"%\n%
      %\n%
      ^>nul set /A "f11=(f1&0x00FFF000)>>12", "f10=f1&0x00000FFF"%\n%
      ^>nul set /A "f21=(f2&0x00FFF000)>>12", "f20=f2&0x00000FFF"%\n%
      ^>nul set /A "AA=f11*f21", "BC=f11*f20", "DE=f10*f21", "FF=f10*f20"%\n%
      ^>nul set /A "B=(BC&0x00FFF000)>>12", "C=BC&0x00000FFF"%\n%
      ^>nul set /A "D=(DE&0x00FFF000)>>12", "E=DE&0x00000FFF"%\n%
      %\n%
      ^>nul set /A "fR0=((C+E)<<12)+FF"%\n%
      ^>nul set /A "fR1=AA+B+D+(fR0>>24)"%\n%
      ^>nul set /A "fR0&=0x00FFFFFF"%\n%
      ^>nul set /A "sR=s1%bOR%s2", "eR=e1+e2"%\n%
      %\n%
      ^>nul set /A "fR1=(fR1<<1)|(fR0>>23)"%\n%
      ^>nul set /A "fR0=(fR0&0x007FFFFF)<<1"%\n%
      %\n%
      for /L %%a in ^(1,1,48^) do @^(%\n%
         if %#%fR1%#% LSS 8388608 ^(%\n%
            if %#%eR%#% GTR -127 ^(%\n%
               ^>nul set /A "fR1=(fR1<<1)|(fR0>>23)"%\n%
               ^>nul set /A "fR0=(fR0&0x007FFFFF)<<1"%\n%
               ^>nul set /A "eR-=1"%\n%
            ^)%\n%
         ^)%\n%
      ^)%\n%
%[%
::"   normalize fR1 to 24 bits (rest := (last 2 bits of) fR0, as (some bits) may disappear)"^
%]%
      set "rest1=fR0"%\n%
      for %%a in ^(1,2^) do @if %#%fR1%#% GEQ 16777216 ^(%\n%
         ^>nul set /A "d=(fR1&1)<<24"%\n%
         ^>nul set /A "eR+=1", "fR1>>=1", "fR0|=d"%\n%
      ^)%\n%
%[%
::"   ensure minimum representable exponent (denormalized number: -127)"^
%]%
      set "rest2=fR0"%\n%
      for /L %%a in ^(%#%eR%#%,1,-128^) do @^(%\n%
         ^>nul set /A "d=(fR1&1)<<24"%\n%
         ^>nul set /A "eR+=1", "fR1>>=1", "fR0|=d"%\n%
      ^)%\n%
%[%
::"   perform rounding"^
%]%
      ^>nul set /A "roundingMode+=0", "r=(fR0&0x00800000)>>23", "rest=fR0&0x7FFFFF"%\n%
      if ^"%#%rest%#%%#%rest1%#%%#%rest2%#%^" == "000" ^( set "rest=0"%\n%
      ^) else set "rest=1"%\n%
      %\n%
      if ^"%#%roundingMode%#%^" == "4" ^(%\n%
%[%
::"         No Rounding mode                                +2.5 +1.5 -1.5 -2.5"^
::"         4  toward -inf        [rounding down, or floor] +2.0 +1.0 -2.0 -3.0"^
%]%
         if ^"%#%rest%#%^" == "1" set "r=1"%\n%
         if ^"%#%sR%#%^" == "1" ^>nul set /A "fR1+=r"%\n%
      ^) else if ^"%#%roundingMode%#%^" == "3" (%\n%
%[%
::"         No Rounding mode                                +2.5 +1.5 -1.5 -2.5"^
::"         3  toward +inf        [rounding up, or ceiling] +3.0 +2.0 -1.0 -2.0"^
%]%
         if ^"%#%rest%#%^" == "1" set "r=1"%\n%
         if ^"%#%sR%#%^" == "0" ^>nul set /A "fR1+=r"%\n%
      ^) else if ^"%#%roundingMode%#%^" == "2" ^(%\n%
%[%
::"         No Rounding mode                                +2.5 +1.5 -1.5 -2.5"^
::"         2  toward 0           [truncation, no rounding] +2.0 +1.0 -1.0 -2.0"^
%]%
         rem nothing left to do%\n%
      ^) else if ^"%#%roundingMode%#%^" == "1" ^(%\n%
%[%
::"         No Rounding mode                                +2.5 +1.5 -1.5 -2.5"^
::"         1  to nearest, ties away from zero              +3.0 +2.0 -2.0 -3.0"^
%]%
         ^>nul set /A "fR1+=r"%\n%
      ^) else ^(%\n%
%[%
::"         No Rounding mode                                +2.5 +1.5 -1.5 -2.5"^
::"         0  to nearest, ties to even           [default] +2.0 +2.0 -2.0 -2.0"^
%]%
         if %#%r%#% == 1 ^(%\n%
            if ^"%#%rest%#%^" == "0" ^(%\n%
               ^>nul set /A "fR1+=(fR1&1)"%\n%
            ^) else ^(%\n%
               ^>nul set /A "fR1+=1"%\n%
            ^)%\n%
         ^)%\n%
      ^)%\n%
%[%
::"   overflow checking"^
%]%
      if %#%fR1%#% GEQ 16777216 ^>nul set /A "eR+=1", "fR1>>=1"%\n%
%[%
::"   build result (denormalized/normalized numbers and check for inf)"^
%]%
      if ^"%#%eR%#%^" == "-127" ^(%\n%
         ^>nul set /A "fR1>>=1"%\n%
      ^) else ^(%\n%
         if %#%eR%#% GEQ 128 ^(%\n%
            ^>nul set /A "fR1=0"%\n%
         ^) else ^(%\n%
            ^>nul set /A "fR1&=0x007FFFFF"%\n%
         ^)%\n%
      ^)%\n%
      ^>nul set /A "e=eR+127"%\n%
      ^>nul set /A "result=(sR<<31)|((eR+127)<<23)|fR1"%\n%
   ^)%\n%
   %\n%
   for %%a in ^(^"%#%result%#%^"^) do @for %%b in ^(^"%#%param[3]:~1%#%^"^) do @^(endlocal ^& ^(if "%%~b" == "" ^( echo %%~a^) else ^(set "%%~b=%%~a"^)^)^)%\n%
^) else setlocal enableDelayedExpansion ^& set params=, 
)
   (set #=)
::
:: end define $floatMul


:: define $intToHex
::   %~1 int32 string value
::   %~2 variable to store the hex value
::   for optical improvement
   (set #=0)
   if "!#!" == "0" (set bOR=^^^^) else (set bOR=^^)
   if "!#!" == "0" (set #=^^^^^^^^^^^^^^^!) else (set #=!)

   setlocal enableExtensions disableDelayedExpansion
   set LF=^


   set ^"\n=^^^%LF%%LF%^%LF%%LF%^<nul ^^^"
   set ^"[=%%~#^<nul ^^^%LF%%LF%^<nul ^^^"
   set ^"]=^<nul^^^%LF%%LF%^%LF%%LF%^<nul ^^^"
   endlocal & (

for %%# in ("") do set $intToHex=@for %%N in ^(0 1^) do @if %%~N == 1 ^(%\n%
   set "N=0"%\n%
   set "param[1]= "%\n%
   set "param[2]= "%\n%
   for %%P in ^(%#%params%#%^) do @^(%\n%
      ^>nul set /A "N+=1"%\n%
      set ^"param[%#%N%#%]= %%~P^"%\n%
   ^)%\n%
   set "N="%\n%
   %\n%
   ^>nul set /A "num=param[1]"%\n%
   set "hex= "%\n%
   set "digits=0123456789ABCDEF"%\n%
   for /L %%a in ^(0,1,7^) do @^(%\n%
      ^>nul set /A "nibble=num&0xF", "num>>=4"%\n%
      for %%b in ^(%#%nibble%#%^) do @set ^"hex=%#%digits:~%%b,1%#%%#%hex%#%^"%\n%
   ^)%\n%
   %\n%
   for %%a in ^(^"0x%#%hex%#%^"^) do @for %%b in ^(^"%#%param[2]:~1%#%^"^) do @^(endlocal ^& ^(if "%%~b" == "" ^( echo %%~a^) else ^(set "%%~b=%%~a"^)^)^)%\n%
^) else setlocal enableDelayedExpansion ^& set params=, 
)
   (set #=)
::
:: end define $intToHex

::
:: All macros loaded to memory: return success (errorLevel == 0).
exit /b 0

:exit

Code: Select all

0x00000000 <-- ".e" --> "0.0"
0x00000000 <-- ".e3" --> "0.0"
0x3E4CCCCD <-- ".2e" --> "0.2"
0x3F800000 <-- "1.e" --> "1.0"
0x00000000 <-- "+.e" --> "0.0"
0x3F800000 <-- "+1.e" --> "1.0"
0x00000000 <-- "-.e" --> "0.0"
0xBF800000 <-- "-1.e" --> "-1.0"
0x7FFFFFFF <-- "NaN        " --> "NaN"
0x7FFFFFFF <-- "+NaN       " --> "NaN"
0xFFFFFFFF <-- "-NaN       " --> "-NaN"
0x7FFFFFFF <-- "+NaN(7FFFFFFF)" --> "NaN"
0xFFFFFFFF <-- "-NaN(FFFFFFFF)" --> "-NaN"
0x7F800000 <-- "inf        " --> "inf"
0x7F800000 <-- "+inf       " --> "inf"
0xFF800000 <-- "-inf       " --> "-inf"
0x00000000 <-- "0.0" --> "0.0"
0x01234567 <-- "0x01234567        " --> "2.99881655e-38"
0x01234567 <-- "+0x01234567       " --> "2.99881655e-38"
0x81234567 <-- "-0x01234567       " --> "-2.99881655e-38"
0x447A0000 <-- "1000.0            " --> "1000.0"
0x447A0001 <-- "1000.00006        " --> "1000.00006"
0x358637BD <-- "0.000001          " --> "1.0e-6"
0x00000001 <-- "1.4e-45           " --> "1.40129846e-45"
0x00000003 <-- "4.2E-45           " --> "4.20389539e-45"
0x00800001 <-- "1.1754945E-38     " --> "1.17549449e-38"
0x00400000 <-- "5.877472E-39      " --> "5.87747175e-39"
0x41460000 <-- "12.375            " --> "12.375"
0x38D1B717 <-- "0.0001            " --> "1.0e-4"
0x3A83126F <-- "0.001             " --> "0.001"
0x3C23D70A <-- "0.01              " --> "0.01"
0x3DCCCCCD <-- "0.1               " --> "0.1"
0x3F800000 <-- "1                 " --> "1.0"
0x41200000 <-- "10                " --> "10.0"
0x42C80000 <-- "100               " --> "100.0"
0x447A0000 <-- "1000              " --> "1000.0"
0x461C4000 <-- "10000             " --> "10000.0"
0x47C35000 <-- "100000            " --> "100000.0"
0x49742400 <-- "1000000           " --> "1000000.0"
0x4B189680 <-- "10000000          " --> "1.0e7"
0x42883EFA <-- "68.123            " --> "68.123"
0x00800000 <-- "1.17549434E-38    " --> "1.17549435e-38"
0x00400000 <-- "5.877472E-39      " --> "5.87747175e-39"
0xB58637BD <-- "-1.0e-6           " --> "-1.0e-6"
0x00C00000 <-- "1.763241500000E-38" --> "1.76324153e-38"
0x00002000 <-- "1.14794E-41       " --> "1.1479437e-41"
0x00000001 <-- "1.4E-45           " --> "1.40129846e-45"
0x501502F9 <-- "1.0e10            " --> "1.0e10"
0x501502F9 <-- "+1.0e+10          " --> "1.0e10"
0xAEDBE6FF <-- "- 1.0 e -10       " --> "-1.0e-10"

Code: Select all

0x00000000 <-- ".e" --> "0.0"
0x00000000 <-- ".e3" --> "0.0"
0x3E4CCCCD <-- ".2e" --> "0.2"
0x3F800000 <-- "1.e" --> "1.0"
0x00000000 <-- "+.e" --> "0.0"
0x3F800000 <-- "+1.e" --> "1.0"
0x00000000 <-- "-.e" --> "0.0"
Ungültige Zahl. Zahlen sind begrenzt auf eine Genauigkeit von 32 Bits.
Fehlender Operand
0.0
0x00000000 <-- "-1.e" --> ""
0x7FFFFFFF <-- "NaN        " --> "NaN"
0x7FFFFFFF <-- "+NaN       " --> "NaN"
Ungültige Zahl. Zahlen sind begrenzt auf eine Genauigkeit von 32 Bits.
Ungültige Zahl. Zahlen sind begrenzt auf eine Genauigkeit von 32 Bits.
Fehlender Operand
0.0
0x00000000 <-- "-NaN       " --> ""
0x7FFFFFFF <-- "+NaN(7FFFFFFF)" --> "NaN"
Ungültige Zahl. Zahlen sind begrenzt auf eine Genauigkeit von 32 Bits.
Ungültige Zahl. Numerische Konstanten sind entweder dezimale (17),
hexadezimale (0x11) oder oktale (021) Zahlen.
Ungültige Zahl. Numerische Konstanten sind entweder dezimale (17),
hexadezimale (0x11) oder oktale (021) Zahlen.
Ungültige Zahl. Numerische Konstanten sind entweder dezimale (17),
hexadezimale (0x11) oder oktale (021) Zahlen.
Ungültige Zahl. Numerische Konstanten sind entweder dezimale (17),
hexadezimale (0x11) oder oktale (021) Zahlen.
Ungültige Zahl. Numerische Konstanten sind entweder dezimale (17),
hexadezimale (0x11) oder oktale (021) Zahlen.
Ungültige Zahl. Numerische Konstanten sind entweder dezimale (17),
hexadezimale (0x11) oder oktale (021) Zahlen.
Ungültige Zahl. Numerische Konstanten sind entweder dezimale (17),
hexadezimale (0x11) oder oktale (021) Zahlen.
Ungültige Zahl. Numerische Konstanten sind entweder dezimale (17),
hexadezimale (0x11) oder oktale (021) Zahlen.
Ungültige Zahl. Numerische Konstanten sind entweder dezimale (17),
hexadezimale (0x11) oder oktale (021) Zahlen.
Ungültige Zahl. Numerische Konstanten sind entweder dezimale (17),
hexadezimale (0x11) oder oktale (021) Zahlen.
Ungültige Zahl. Numerische Konstanten sind entweder dezimale (17),
hexadezimale (0x11) oder oktale (021) Zahlen.
Ungültige Zahl. Numerische Konstanten sind entweder dezimale (17),
hexadezimale (0x11) oder oktale (021) Zahlen.
Ungültige Zahl. Numerische Konstanten sind entweder dezimale (17),
hexadezimale (0x11) oder oktale (021) Zahlen.
Ungültige Zahl. Numerische Konstanten sind entweder dezimale (17),
hexadezimale (0x11) oder oktale (021) Zahlen.
Ungültige Zahl. Numerische Konstanten sind entweder dezimale (17),
hexadezimale (0x11) oder oktale (021) Zahlen.
Ungültige Zahl. Numerische Konstanten sind entweder dezimale (17),
hexadezimale (0x11) oder oktale (021) Zahlen.
Ungültige Zahl. Numerische Konstanten sind entweder dezimale (17),
hexadezimale (0x11) oder oktale (021) Zahlen.
Ungültige Zahl. Numerische Konstanten sind entweder dezimale (17),
hexadezimale (0x11) oder oktale (021) Zahlen.
Ungültige Zahl. Numerische Konstanten sind entweder dezimale (17),
hexadezimale (0x11) oder oktale (021) Zahlen.
Ungültige Zahl. Numerische Konstanten sind entweder dezimale (17),
hexadezimale (0x11) oder oktale (021) Zahlen.
Ungültige Zahl. Numerische Konstanten sind entweder dezimale (17),
hexadezimale (0x11) oder oktale (021) Zahlen.
Ungültige Zahl. Numerische Konstanten sind entweder dezimale (17),
hexadezimale (0x11) oder oktale (021) Zahlen.
Ungültige Zahl. Numerische Konstanten sind entweder dezimale (17),
hexadezimale (0x11) oder oktale (021) Zahlen.
Ungültige Zahl. Numerische Konstanten sind entweder dezimale (17),
hexadezimale (0x11) oder oktale (021) Zahlen.
Ungültige Zahl. Numerische Konstanten sind entweder dezimale (17),
hexadezimale (0x11) oder oktale (021) Zahlen.
Ungültige Zahl. Numerische Konstanten sind entweder dezimale (17),
hexadezimale (0x11) oder oktale (021) Zahlen.
Ungültige Zahl. Numerische Konstanten sind entweder dezimale (17),
hexadezimale (0x11) oder oktale (021) Zahlen.
Ungültige Zahl. Numerische Konstanten sind entweder dezimale (17),
hexadezimale (0x11) oder oktale (021) Zahlen.
Ungültige Zahl. Numerische Konstanten sind entweder dezimale (17),
hexadezimale (0x11) oder oktale (021) Zahlen.
Ungültige Zahl. Numerische Konstanten sind entweder dezimale (17),
hexadezimale (0x11) oder oktale (021) Zahlen.
Ungültige Zahl. Numerische Konstanten sind entweder dezimale (17),
hexadezimale (0x11) oder oktale (021) Zahlen.
Ungültige Zahl. Numerische Konstanten sind entweder dezimale (17),
hexadezimale (0x11) oder oktale (021) Zahlen.
Ungültige Zahl. Numerische Konstanten sind entweder dezimale (17),
hexadezimale (0x11) oder oktale (021) Zahlen.
Ungültige Zahl. Numerische Konstanten sind entweder dezimale (17),
hexadezimale (0x11) oder oktale (021) Zahlen.
Ungültige Zahl. Numerische Konstanten sind entweder dezimale (17),
hexadezimale (0x11) oder oktale (021) Zahlen.
Ungültige Zahl. Numerische Konstanten sind entweder dezimale (17),
hexadezimale (0x11) oder oktale (021) Zahlen.
Ungültige Zahl. Numerische Konstanten sind entweder dezimale (17),
hexadezimale (0x11) oder oktale (021) Zahlen.
Ungültige Zahl. Numerische Konstanten sind entweder dezimale (17),
hexadezimale (0x11) oder oktale (021) Zahlen.
Ungültige Zahl. Zahlen sind begrenzt auf eine Genauigkeit von 32 Bits.
Fehlender Operand
0.0
0x00000000 <-- "-NaN(FFFFFFFF)" --> ""
0x7F800000 <-- "inf        " --> "inf"
0x7F800000 <-- "+inf       " --> "inf"
Ungültige Zahl. Zahlen sind begrenzt auf eine Genauigkeit von 32 Bits.
Ungültige Zahl. Zahlen sind begrenzt auf eine Genauigkeit von 32 Bits.
Fehlender Operand
0.0
0x00000000 <-- "-inf       " --> ""
0x00000000 <-- "0.0" --> "0.0"
0x01234567 <-- "0x01234567        " --> "2.99881655e-38"
0x01234567 <-- "+0x01234567       " --> "2.99881655e-38"
Ungültige Zahl. Zahlen sind begrenzt auf eine Genauigkeit von 32 Bits.
Ungültige Zahl. Zahlen sind begrenzt auf eine Genauigkeit von 32 Bits.
Fehlender Operand
0.0
0x00000000 <-- "-0x01234567       " --> ""
0x447A0000 <-- "1000.0            " --> "1000.0"
0x447A0001 <-- "1000.00006        " --> "1000.00006"
0x358637BD <-- "0.000001          " --> "1.0e-6"
0x00000001 <-- "1.4e-45           " --> "1.40129846e-45"
0x00000003 <-- "4.2E-45           " --> "4.20389539e-45"
0x00800001 <-- "1.1754945E-38     " --> "1.17549449e-38"
0x00400000 <-- "5.877472E-39      " --> "5.87747175e-39"
0x41460000 <-- "12.375            " --> "12.375"
0x38D1B717 <-- "0.0001            " --> "1.0e-4"
0x3A83126F <-- "0.001             " --> "0.001"
0x3C23D70A <-- "0.01              " --> "0.01"
0x3DCCCCCD <-- "0.1               " --> "0.1"
0x3F800000 <-- "1                 " --> "1.0"
0x41200000 <-- "10                " --> "10.0"
0x42C80000 <-- "100               " --> "100.0"
0x447A0000 <-- "1000              " --> "1000.0"
0x461C4000 <-- "10000             " --> "10000.0"
0x47C35000 <-- "100000            " --> "100000.0"
0x49742400 <-- "1000000           " --> "1000000.0"
0x4B189680 <-- "10000000          " --> "1.0e7"
0x42883EFA <-- "68.123            " --> "68.123"
0x00800000 <-- "1.17549434E-38    " --> "1.17549435e-38"
0x00400000 <-- "5.877472E-39      " --> "5.87747175e-39"
Ungültige Zahl. Zahlen sind begrenzt auf eine Genauigkeit von 32 Bits.
Fehlender Operand
0.0
0x00000000 <-- "-1.0e-6           " --> ""
0x00C00000 <-- "1.763241500000E-38" --> "1.76324153e-38"
0x00002000 <-- "1.14794E-41       " --> "1.1479437e-41"
0x00000001 <-- "1.4E-45           " --> "1.40129846e-45"
0x501502F9 <-- "1.0e10            " --> "1.0e10"
0x501502F9 <-- "+1.0e+10          " --> "1.0e10"
Ungültige Zahl. Zahlen sind begrenzt auf eine Genauigkeit von 32 Bits.
Fehlender Operand
0.0
0x00000000 <-- "- 1.0 e -10       " --> ""

Code: Select all

set "iPart=0xFFFFFFFF"
set /A "s=0x80000000"
set /A "float=%s%|0x7FFFFFFF"
set /A "float=%s%|0x7F800000"
set /A "float=%s%^%iPart%"

Code: Select all

:: perform rounding: to nearest, ties to even
....
set /A "float=-2147483648|1065353216|0"

Code: Select all

> set "iPart=0xFFFFFFFF"

> set /A "s=0x80000000"

> set /A "float=-2147483648|0x7FFFFFFF"
Ungültige Zahl. Zahlen sind begrenzt auf eine Genauigkeit von 32 Bits.

> set /A "float=-2147483648|0x7F800000"
Ungültige Zahl. Zahlen sind begrenzt auf eine Genauigkeit von 32 Bits.

> set /A "float=-2147483648^0xFFFFFFFF"
Ungültige Zahl. Zahlen sind begrenzt auf eine Genauigkeit von 32 Bits.

Code: Select all

C:\temp>set /a b=-2147483648
Ungültige Zahl. Zahlen sind begrenzt auf eine Genauigkeit von 32 Bits.

Code: Select all

C:\temp>set /a var1=0x80000000
-2147483648
C:\temp>set /a var2=var1
-2147483648
C:\temp>set /a var3=%var1%
Ungültige Zahl. Zahlen sind begrenzt auf eine Genauigkeit von 32 Bits.

Code: Select all

   set /A "float=%s%|%e%|%f%"

Code: Select all

   set /A "float=s|e|f"

Code: Select all

set "iPart=0xFFFFFFFF"
set "s=0x80000000"
set /A "float=%s%|0x7FFFFFFF"
set /A "float=%s%|0x7F800000"
set /A "float=%s%^%iPart%"

:: or that
set "iPart=0xFFFFFFFF"
set /A "s=0x80000000"
set /A "float=s|0x7FFFFFFF"
set /A "float=s|0x7F800000"
set /A "float=s^iPart"

Code: Select all

@prompt $g
setlocal
set "iPart=0xFFFFFFFF"
set "s=0x80000000"
set /A "float=%s%|0x7FFFFFFF"
rem %float%
set /A "float=%s%|0x7F800000"
rem %float%
set /A "float=%s%^%iPart%"
rem %float%
endlocal
rem ~~~~~~~~~~~~~~~~~~~~~
setlocal
set "iPart=0xFFFFFFFF"
set /A "s=0x80000000"
set /A "float=s|0x7FFFFFFF"
rem %float%
set /A "float=s|0x7F800000"
rem %float%
set /A "float=s^iPart"
rem %float%
endlocal
pause

Code: Select all

>setlocal

>set "iPart=0xFFFFFFFF"

>set "s=0x80000000"

>set /A "float=0x80000000|0x7FFFFFFF"

>rem -1

>set /A "float=0x80000000|0x7F800000"

>rem -8388608

>set /A "float=0x80000000^0xFFFFFFFF"

>rem 2147483647

>endlocal

>rem ~~~~~~~~~~~~~~~~~~~~~

>setlocal

>set "iPart=0xFFFFFFFF"

>set /A "s=0x80000000"

>set /A "float=s|0x7FFFFFFF"

>rem -1

>set /A "float=s|0x7F800000"

>rem -8388608

>set /A "float=s^iPart"

>rem -1

>endlocal

>pause
Drücken Sie eine beliebige Taste . . .

Code: Select all

@prompt $g &setlocal
set "iPart=0xFFFFFFFF"
set "s=0x80000000"
set /A "float=s|0x7FFFFFFF"
rem %float%
set /A "float=s|0x7F800000"
rem %float%
set /A "float=s^%iPart%"
rem %float%
pause

Code: Select all

> set "iPart=0xFFFFFFFF"

> set "s=0x80000000"

> set /A "float=s|0x7FFFFFFF"

> rem 2147483647

> set /A "float=s|0x7F800000"

> rem 2147483647

> set /A "float=s^0xFFFFFFFF"

> rem -2147483648

> pause
Drücken Sie eine beliebige Taste . . .

Code: Select all

@echo off
cls
call :floatTest ".e"
call :floatTest ".e3"
call :floatTest ".2e"
call :floatTest "1.e"
call :floatTest "+.e"
call :floatTest "+1.e"
call :floatTest "-.e"
call :floatTest "-1.e"

call :floatTest "NaN        "
call :floatTest "+NaN       "
call :floatTest "-NaN       "
call :floatTest "+NaN(7FFFFFFF)"
call :floatTest "-NaN(FFFFFFFF)"

call :floatTest "inf        "
call :floatTest "+inf       "
call :floatTest "-inf       "

call :floatTest "0.0"

call :floatTest "0x01234567        "
call :floatTest "+0x01234567       "
call :floatTest "-0x01234567       "

call :floatTest "1000.0            "
call :floatTest "1000.00006        "

call :floatTest "0.000001          "
call :floatTest "1.4e-45           "
call :floatTest "4.2E-45           "
call :floatTest "1.1754945E-38     "
call :floatTest "5.877472E-39      "
call :floatTest "12.375            "

call :floatTest "0.0001            "
call :floatTest "0.001             "
call :floatTest "0.01              "
call :floatTest "0.1               "
call :floatTest "1                 "
call :floatTest "10                "
call :floatTest "100               "
call :floatTest "1000              "
call :floatTest "10000             "
call :floatTest "100000            "
call :floatTest "1000000           "
call :floatTest "10000000          "

call :floatTest "68.123            "
call :floatTest "1.17549434E-38    "
call :floatTest "5.877472E-39      "

call :floatTest "-1.0e-6           "

call :floatTest "1.763241500000E-38"
call :floatTest "1.14794E-41       "

call :floatTest "1.4E-45           "


call :floatTest "1.0e10            "
call :floatTest "+1.0e+10          "
call :floatTest "- 1.0 e -10       "

goto :eof


:floatTest
::   %~1 float string
::   %~2 variable to store the resulting int coding of the float in hexadecimal representation if present,
::       else echo hex value if undefined
   setlocal enableDelayedExpansion
   set "float="

   call :str2float "%~1" float
   call :intToHex hex "%float%"

   call :float2str %float% string

   endlocal & if "%~2" == "" ( echo %hex% ^<-- "%~1" --^> "%string%" ) else ( set "%~2=%hex%" --^> "%string%" )
   goto :eof



:intToHex
::   %~1 variable to store the hex value
::   %~2 int32 string value
::   needed only to simulate the "random_pass=$(dd..." line in procedure ":do_a_file"
   setlocal enableDelayedExpansion
   set /A "num=%~2"
   set "hex="
   set "digits=0123456789ABCDEF"
   for /L %%a in (0,1,7) do (
      set /A "nibble=num&0xF", "num>>=4"
      for %%b in (!nibble!) do set "hex=!digits:~%%b,1!!hex!"
   )
   endlocal & set "%~1=0x%hex%"
   goto :eof


:intToHex
::   %~1 variable to store the hex value
::   %~2 int32 string value
::   needed only to simulate the "random_pass=$(dd..." line in procedure ":do_a_file"
   setlocal enableDelayedExpansion
   set /A "num=%~2"
   set "hex="
   set "digits=0123456789ABCDEF"
   for /L %%a in (0,1,7) do (
      set /A "nibble=num&0xF", "num>>=4"
      for %%b in (!nibble!) do set "hex=!digits:~%%b,1!!hex!"
   )
   endlocal & set "%~1=0x%hex%"
   goto :eof


:: Rounding to integers using the IEEE 754 rules
:: No Rounding mode                                +2.5 +1.5 -1.5 -2.5
:: 0  to nearest, ties to even           (default) +2.0 +2.0 -2.0 -2.0
:: 1  to nearest, ties away from zero (truncation) +3.0 +2.0 -2.0 -3.0
:: 2  toward 0                                     +2.0 +1.0 -1.0 -2.0
:: 3  toward +inf        (rounding up, or ceiling) +3.0 +2.0 -1.0 -2.0
:: 4  toward -inf        (rounding down, or floor) +2.0 +1.0 -2.0 -3.0
::
:str2float
::   %~1 float string
::   %~2 variable to store the resulting int coding of the float
::   actually there is no error detection,
::   so assumed: no errorneous strings
::   set "inf=0x7F800000"
::   set "nan=0x7FFFFFFF"
::   ignore NaN(...), +NaN(...), -NaN(...) format: NaN, +NaN, -NaN watched
::   "", "+", "NaN", "+NaN" ->  NaN == 0x7FFFFFFF == 2147483647
::   "-", "-NaN"            -> -NaN == 0xFFFFFFFF == -1
::   "inf", "+inf"          ->  inf == 0x7F800000 == 2139095040
::   "-inf"                 -> -inf == 0xFF800000 == -8388608
::
   if "%~2" == "" exit /b 1
   if "%~1" == "" set /A "%~2=0x7FFFFFFF" & exit /b 0
   
   setlocal enableDelayedExpansion

::   divide in parts: sPart * iPart.fPart * 10^^ePart
   set "string=%~1"
   set "string= %string: =%"
   set "float="

   set "ePart=%string:*e=%"
   if "%string%" == "%ePart%" set "ePart="
   set "string=!string:e%ePart%=!"
   if not defined ePart set "ePart=0"

   set "fPart=%string:*.=%"
   if "%string%" == "%fPart%" set "fPart="
   set "string=!string:.%fPart%=!"
   if "%fPart%" == "" set "fPart=0"

   if "%string:~1,1%" == "-" (
      set "iPart=%string:~2%"
      set "sPart=-1"
   )else if "%string:~1,1%" == "+" (
      set "iPart=%string:~2%"
      set "sPart=1"
   ) else (
      set "iPart=%string:~1%"
      set "sPart=1"
   )
   if not defined iPart set "iPart=0"

::   set sign flag (s)
   if %sPart% == -1 ( set /A "s=0x80000000" ) else ( set "s=0" )

::   detect NaN, inf and hex format
   if "%iPart:~0,3%" == "NaN" ( set /A "float=s|0x7FFFFFFF"
   ) else if "%iPart:~0,3%" == "inf" ( set /A "float=s|0x7F800000"
   ) else if "%iPart:~0,2%" == "0x" ( set /A "float=s ^ iPart"
   )
   if defined float (endlocal & (if "%~2" == "" ( echo(%float%) else (set "%~2=%float%")) & goto :eof)

::   normalize to: sPart * 0.significand * 10^ePart, 0.significand >= 0.1
::   AND
::   detect 0.0
   for /F "tokens=* delims= " %%a in ("%iPart:0= %") do set "iPartP=%%~a"
   if defined iPartP (
      set "iPartP=!iPartP: =0!"
      set "string= !iPart!"
      for %%a in (4096,2048,1024,512,256,128,64,32,16,8,4,2,1) do (
         if not "!string:~%%a,1!" == "" (
            set "string=!string:~%%a!"
            set /A "ePart+=%%a"
         )
      )
      set "significand=!iPartP!!fPart!"
      set "iPartP="
   ) else (
      for /F "tokens=* delims= " %%a in ("%fPart:0= %") do set "fPartP=%%~a"
      if defined fPartP (
         set "fPartP=!fPartP: =0!"
         for %%a in (!fPartP!) do set "string= !fPart:%%a=!"
         for %%a in (4096,2048,1024,512,256,128,64,32,16,8,4,2,1) do (
            if not "!string:~%%a,1!" == "" (
               set "string=!string:~%%a!"
               set /A "ePart-=%%a"
            )
         )
         set "significand=!fPartP!"
         set "fPartP="
      ) else ( set /A "float=0"
      )
   )
   if defined float (endlocal & (if "%~2" == "" ( echo(%float%) else (set "%~2=%float%")) & goto :eof)

::   drop unneeded digits
::   transform to: sPart * high_{8}.high_{7-0}low{7-0} * 5^ePart * 2^e_2
   set "significand=%significand:~0,17%0000000000000000"
   set "high=%significand:~0,9%"
   set /A "ePart-=1"
   set /a "e_2=ePart"
   set "low=%significand:~9,8%"

   for %%a in (9 4 2) do (
      set /A "c=high&1"
      if !high! GEQ 200000000 (
         set /A "high>>=1", "low=!c!!low!>>1", "e_2+=1"
         set "low=00000000!low!"
         set "low=!low:~-8!"
      )
   )


::   transform to: sPart * high_{8}.high_{7-0}low{7-0} * 2^e_2
   if %ePart% LSS 0 (
      for /L %%a in (%ePart%,1,-1) do (
         set /A "ePart+=1"
         set /A "c=!high:~-1!%%5"
         set /A "cc=c+1"

         if !high! LSS 125000000 (
            set /A "high=(((!high!-c)/5)<<3)", "e_2-=3", "ePart+=1"
            set /A "low=((!cc!!low!-100000000)/5)<<3"
         ) else (
            set /A "high=(((!high!-c)/5)<<2)", "e_2-=2", "ePart+=1"
            set /A "low=((!cc!!low!-100000000)/5)<<2"
         )

         if !low! GEQ 100000000 (
            set "c=!low:~0,1!"
            set "low=!low:~1!"
            set /A "high+=c"
         )

         set "low=00000000!low!"
         set "low=!low:~-8!"
      )
   ) else if %ePart% GTR 0 (
      for /L %%a in (%ePart%,-1,1) do (
         set /A "c=!high!&7"
         set /A "cc=c+1"

         if !high! LSS 160000000 (
            set /A "high=(((!high!-c)>>2)*5)", "e_2+=2", "ePart-=1"
            set /A "low=((!cc!!low!-100000000)>>2)*5"
         ) else (
            set /A "high=(((!high!-c)>>3)*5)", "e_2+=3", "ePart-=1"
            set /A "low=((!cc!!low!-100000000)>>3)*5"
         )

         if !low! GEQ 100000000 (
            set "c=!low:~0,1!"
            set "low=!low:~1!"
            set /A "high+=c"
         )

         set "low=00000000!low!"
         set "low=!low:~-8!"
      )
   )
   set "f=0"
   for /L %%a in (0, 1 24) do (
      if !high! GEQ 100000000 (
         set /A "f=(f<<1)+1", "high=(!high!-100000000)<<1"
      ) else (
         set /A "high<<=1", "f<<=1"
      )
      set /A "low=(1!low!-100000000)<<1"
      if !low! GEQ 100000000 (
         set "low=!low:~1!"
         set /A "high+=1"
      )
      set "low=00000000!low!"
      set "low=!low:~-8!"
   )

:: set uo round bit (r) that specifies if rounding is performed, and
:: if number is greater that the round bit (rUp: true==1 false==0); this means more bits or decimal digits are available
   set /A "r=f&1"
   set /A "f>>=1"
   set "rUp=1"
   if %high% == 0 if 1%low% == 100000000 set "rUp=0"
   

:: build float
   if %e_2% LEQ -127 (
      set "test=0"
      for /L %%a in (%e_2%,1,-127) do (
         if r == 1 set "rUp=1"
         set /A "r=f&1"
         set /A "f>>=1"
      )
      set /A "e_2=-127"
   ) else (
      if %e_2% GTR 128 (
         set "e_2=128"
      )
   )

:: perform rounding: to nearest, ties to even
   if %r% == 1 (
      if %rUp% == 1 (
         set /A "f+=1"
      ) else (
         set /A "l=f&1"
         if !l! == 1 (
            set /A "f+=1"
         )
      )
   )

   if %e_2% == -127 (
      if %f% == 8388608 set /A "e_2+=1"
   ) else (
      if %f% == 16777216 (
         set /A "e_2+=1"
         set /A "f>>=1"
      )
   )

   set /A "e=(e_2+127)<<23"
   if %e% == 255 ( set "f=0" ) else ( set /A "f&=0x007FFFFF" )
   set /A "float=s|e|f"


   endlocal & (if "%~2" == "" ( echo(%float% %~2) else (set "%~2=%float%"))
   goto :eof


:float2str
::   %~1 float value (int coding)
::   %~2 variable to store the resulting string if exists,
::       else echo string value if undefined
   setlocal enableDelayedExpansion

::   transform to: sPart * high_{8}.high_{7-0}low{7-0} * 2^e
   set "float=%~1"
   set /A "s=(float>>31)&1", "e_2=((float>>23)&0x000000FF)-127", "f=float&0x007FFFFF"
   if %s% == 1 ( set "sPart=-1" ) else ( set "sPart=1" )


   if %e_2% == -127 (
      if !f! == 0 endlocal & (if "%~2" == "" ( echo 0.0) else (set "%~2=0.0")) & goto :eof

      for /L %%a in (0,1,23) do (
         if !f! LSS 8388608 (
            set /A "e_2-=1", "f<<=1"
         )
      )
      set /A "e_2+=1"
   ) else (
      if %e_2% == 128 (
         if %f% == 0 ( endlocal & (if "%~2" == "" ( echo %sPart:1=%inf) else (set "%~2=%sPart:1=%inf")) & goto :eof
         ) else ( endlocal & (if "%~2" == "" ( echo %sPart:1=%NaN) else (set "%~2=%sPart:1=%NaN")) & goto :eof
         )
      )
      set /A "f|=0x00800000"
   )

   set "high=0"
   set "low=00000000"
   for /L %%a in (0, 1, 23) do (
      set /A "b=f&1"
      set /A "f>>=1"
      set /A "c=high&1"
      set "d=!low:~0,1!"

      if !c! == 0 (
         set /A "low=(1!low!-100000000)>>1"
      ) else (
         set /A "low=(!c!!low!)>>1"
      )

      set "low=00000000!low!"
      set "low=!low:~-8!"
      set /A "high>>=1"
      if !b! == 1 set /A "high+=100000000"
   )

::   transform to: sPart * high_{8}.high_{7-0}low{7-0} * 10^ePart
   set "ePart=0"
   if %e_2% GTR 0 (
      set /A "N=(e_2>>1)+1"
      for /L %%a in (!N!,-1,1) do (
         if !e_2! GTR !ePart! (
            set /A "c=!high:~-1!%%5"
            set /A "cc=c+1"

            if !high! LSS 125000000 (
               set /A "high=(((!high!-c)/5)<<3)", "e_2-=3", "ePart+=1"
               set /A "low=((!cc!!low!-100000000)/5)<<3"
            ) else (
               set /A "high=(((!high!-c)/5)<<2)", "e_2-=2", "ePart+=1"
               set /A "low=((!cc!!low!-100000000)/5)<<2"
            )

            if !low! GEQ 100000000 (
               set "c=!low:~0,1!"
               set "low=!low:~1!"
               set /A "high+=c"
            )

            set "low=00000000!low!"
            set "low=!low:~-8!"
         )
      )

      set /A "e_2-=ePart"
      if !e_2! LSS 0 (
         set /A "c=!high:~-1!&((1<<(-e_2))-1)"
         set /A "cc=c+1"
         set /A "high=((!high!-c)>>(-e_2))"
         set /A "low=((!cc!!low!-100000000)>>(-e_2))"
         set "low=00000000!low!"
         set "low=!low:~-8!"
         set "e_2=0"
      )

      if !high! LSS 1000000000 (
         set "high=!high!!low:~0,1!"
         set "low=!low:~1!0"
         set /A "ePart-=1"
      )
   ) else if %e_2% LSS 0 (
      set /A "N=(e_2>>1)-1"
      for /L %%a in (!N!,1,-1) do (
         if !e_2! LSS !ePart! (
            set /A "c=!high!&7"
            set /A "cc=c+1"

            if !high! LSS 160000000 (
               set /A "high=(((!high!-c)>>2)*5)", "e_2+=2", "ePart-=1"
               set /A "low=((!cc!!low!-100000000)>>2)*5"
            ) else (
               set /A "high=(((!high!-c)>>3)*5)", "e_2+=3", "ePart-=1"
               set /A "low=((!cc!!low!-100000000)>>3)*5"
            )
            if !low! GEQ 100000000 (
               set "c=!low:~0,1!"
               set "low=!low:~1!"
               set /A "high+=c"
            )
            set "low=00000000!low!"
            set "low=!low:~-8!"
         )
      )

      set /A "e_2-=ePart"
      if !e_2! GTR 0 (
         set /A "high<<=e_2", "low=((1!low!-100000000)<<e_2)"

         if !low! GEQ 100000000 (
            set /A "high+=!low:~0,1!"
            set "low=!low:~1!"
         ) else (
            set "low=00000000!low!"
            set "low=!low:~-8!"
         )

         set "e_2=0"
      )
   )

:: perform rounding: to nearest, ties to even (9th digit)
   set "r=0"
   set "rUp=0"
   if %low:~0,1% GEQ 5 set "r=1"
   if %low:~0,1% GTR 5 set "rUp=1"
   if 1%low:~1% GTR 10000000 set "rUp=1"

   if %r% == 1 (
      if %rUp% == 1 (
         set /A "high+=1"
      ) else (
         set /A "l=f&1"
         if !l! == 1 (
            set /A "high+=1"
         )
      )
   )

::perform rounding to 'nice' numbers 1: last 3 digits <= '005'
   if 1%high:~-3% LEQ 1005 set "high=%high:~0,-1%0"


::perform rounding to 'nice' numbers 2: last 4 digits <= '0050'
   if 1%high:~-4% LEQ 10050 set "high=%high:~0,-2%00"

::perform rounding to 'nice' numbers 3: last 3 digits >= '995'
   if 1%high:~-3% GEQ 1995 (
      set "high=%high:~0,-1%9"
      set /A "high+=1"
   )

::perform rounding to 'nice' numbers 4: last 4 digits >= '9950'
   if 1%high:~-4% GEQ 19950 (
      set "high=%high:~0,-2%99"
      set /A "high+=1"
   )

:: overflow checking
   if %high% GEQ 1000000000 (
      set "high=%high:~0,-1%"
      set /A "ePart+=1"
   )

::perform using 'nice' numbers 1: no trailing zeroes, except if none exits prior or after the seperator
   for /L %%a in (1,1,8) do (
      if defined high (
         if !high:~-1! == 0 (
             set "high=!high:~0,-1!"
         )
      )
   )


::perform using 'nice' numbers 2: 6 digits prior to separator or 3 digits after are allowed to avoid 'e'
   set "integer=%high:~0,1%"
   set "fraction=%high:~1%"


   if -4 LSS %ePart% if %ePart% LSS 7 (
      if %ePart% LSS 0 (
         set "integer=00%integer%"
         set "fraction=!integer:~%ePart%!"
         set "integer=0"
         set "ePart=0"
      ) else if 0 LSS %ePart% (
         if defined fraction (
            set "integer=%integer%!fraction:~0,%ePart%!"
            set "fraction=!fraction:~%ePart%!"
            set "ePart=0"
         ) else (
            set "fraction=000000"
            set "integer=%integer%!fraction:~0,%ePart%!"
            set "fraction="
            set "ePart=0"
         )
      )
   )

::perform using 'nice' numbers 3: avoid lonely separator
   if not defined integer set "integer=0"
   if not defined fraction set "fraction=0"

   set "string="
   if %sPart% == -1 set "string=-"
   set "string=%string%%integer%.%fraction%"
   if not %ePart% == 0 set "string=%string%e%ePart%"

   endlocal & (if "%~2" == "" ( echo(%string% %~2) else (set "%~2=%string%"))
   goto :eof