[数值计算] 批处理实现浮点运算

buyiyang

批处理不能进行浮点运算是一大憾事，便起念写一个算法支持浮点，已经写了加法和乘法，加法比较简单，不限位数，乘法是通过二进制进行计算的，会有一定误差，同样不限位数。分享一下，望指教。
更新：添加了除法和求平方根，限制位数。
因帖子字数限制，分为两部分，此为第一部分，三楼为第二部分。

@echo off
set "input=%~1"
if "%input%"=="" echo,输入为空&exit /b
set "input=%input: =%"
if "%input%"=="" echo,输入为空&exit /b
setlocal enabledelayedexpansion
for /f "tokens=1-2 delims=+-*/" %%i in ("%input%") do (
    if not "%%j"=="" (set "p1=%%i"&set "p2=%%j") else set "p1=%%i"
    for /f "tokens=1-2 delims=0123456789." %%i in ("%input%") do set "op=%%i%%j"
    if "!op!"=="+" (call :add "!p1!" "!p2!"&echo,!add_result!) else if "!op!"=="-" (
    echo,减法) else if "!op!"=="*" (call :mul "!p1!" "!p2!"&echo,!mul_result!) else if "!op!"=="/" (
    call :div "!p1!" "!p2!"&echo,!quo_result!) else if "!op!"=="" (call :sqrt "!p1!"&echo,!sqrt_result!) else (echo,操作符错误)
    )
exit /b

:add
setlocal
for /f "tokens=1-2 delims=." %%i in ("%~1") do (
    set "p1_int=%%i"
    if "%%j"=="" (set /a p1_fd=0) else set "p1_fd=%%j"
    )
for /f "tokens=1-2 delims=." %%i in ("%~2") do (
    set "p2_int=%%i"
    if "%%j"=="" (set /a p2_fd=0) else set "p2_fd=%%j"
    )

call :strlen "%p1_fd%"
set /a p1_fd_len=%len%
call :strlen "%p2_fd%"
set /a p2_fd_len=%len%
if %p1_fd_len% geq %p2_fd_len% (set /a fd_len_max=p1_fd_len) else set /a fd_len_max=p2_fd_len
set "zero_fill="
for /l %%i in (1,1,%fd_len_max%) do set "zero_fill=!zero_fill!0"
set "p1_fd=%p1_fd%%zero_fill%"&set "p1_fd=!p1_fd:~0,%fd_len_max%!"
set "p2_fd=%p2_fd%%zero_fill%"&set "p2_fd=!p2_fd:~0,%fd_len_max%!"
set /a carry=0
set "fd_dec="
for /l %%i in (-1,-1,-%fd_len_max%) do (
    set /a dec_place=!p1_fd:~%%i,1!+!p2_fd:~%%i,1!+!carry!
    if !dec_place! geq 10 (set /a carry=dec_place/10,dec_place=dec_place-10) else set /a carry=0
    set "fd_dec=!dec_place!!fd_dec!"
    )

call :strlen "%p1_int%"
set /a p1_int_len=%len%
call :strlen "%p2_int%"
set /a p2_int_len=%len%
if %p1_int_len% geq %p2_int_len% (set /a int_len_max=p1_int_len) else set /a int_len_max=p2_int_len
set "zero_fill="
for /l %%i in (1,1,%int_len_max%) do set "zero_fill=!zero_fill!0"
set "p1_int=%zero_fill%%p1_int%"&set "p1_int=!p1_int:~-%int_len_max%!"
set "p2_int=%zero_fill%%p2_int%"&set "p2_int=!p2_int:~-%int_len_max%!"
set "int_dec="
for /l %%i in (-1,-1,-%int_len_max%) do (
    set /a dec_place=!p1_int:~%%i,1!+!p2_int:~%%i,1!+!carry!
    if !dec_place! geq 10 (set /a carry=dec_place/10,dec_place=dec_place-10) else set /a carry=0
    set "int_dec=!dec_place!!int_dec!"
    )
if %carry% gtr 0 set "int_dec=%carry%%int_dec%"
if %int_dec% equ 0 (set /a int_dec=0) else for /f "tokens=* delims=0" %%i in ("%int_dec%") do set "int_dec=%%i"
endlocal&set "add_result=%int_dec%.%fd_dec%"&set "int_dec=%int_dec%"&set "fd_dec=%fd_dec%"
goto :eof

:mul
setlocal
for /f "tokens=1-2 delims=." %%i in ("%~1") do (
    set "p1_int=%%i"
    if "%%j"=="" (set /a p1_fd=0) else set "p1_fd=%%j"
    )
for /f "tokens=1-2 delims=." %%i in ("%~2") do (
    set "p2_int=%%i"
    if "%%j"=="" (set /a p2_fd=0) else set "p2_fd=%%j"
    )
call :int2bin "%p1_int%"
set "p1_int_bin=%int_bin%"
call :int2bin "%p2_int%"
set "p2_int_bin=%int_bin%"

call :fd2bin "%p1_fd%"
set "p1_fd_bin=%fd_bin%"
call :fd2bin "%p2_fd%"
set "p2_fd_bin=%fd_bin%"

set "p1_conbin=%p1_int_bin%%p1_fd_bin%"
set "p2_conbin=%p2_int_bin%%p2_fd_bin%"
rem echo,%p1_conbin%
rem echo,%p2_conbin%
set /a acc=0
call :strlen "%p1_conbin%"
set /a p1_conbin_len=%len%
set "p2_conbin_shift=%p2_conbin%"
for /l %%i in (-1,-1,-%p1_conbin_len%) do (
    if "!p1_conbin:~%%i,1!"=="1" (call :add_bin "!acc!" "!p2_conbin_shift!")
    set "acc=!add_bin_result!"
    set "p2_conbin_shift=!p2_conbin_shift!0"
    )
set "acc=%acc:~0,-32%"
call :strlen "%acc%"
set /a acc_len=%len%
if %acc_len% lss 33 (
    set "zero_fill="
    for /l %%i in (1,1,33) do set "zero_fill=!zero_fill!0"
    set "acc=!zero_fill!!acc!"
    )
set "acc_fd=%acc:~-32%"
set "acc_int=%acc:~0,-32%"
if %acc_int% equ 0 (set /a acc_int=0) else (
    for /f "tokens=* delims=0" %%i in ("%acc_int%") do set "acc_int=%%i"
    )
set "acc_int_fd=%acc_int%.%acc_fd%"
rem echo,%acc_int_fd%
call :bin2dec "%acc_int%" "%acc_fd%"
endlocal&set "mul_result=%bin2dec_result%"
goto :eof

:div
setlocal
for /f "tokens=1-2 delims=." %%i in ("%~1") do (
    set /a p1_int_div=%%i
    if "%%j"=="" (set /a p1_fd_div_len=0) else (
        set "p1_fd_div=%%j"
        call :strlen "%%j"
        set /a p1_fd_div_len=len
        )
    )
for /f "tokens=* delims=0" %%i in ("%p1_fd_div%") do if %%i equ 0 (set /a p1_fd_div=0) else set /a p1_fd_div=%%i
for /f "tokens=1-2 delims=." %%i in ("%~2") do (
    call :strlen "%%j"
    set /a p2_div_fd_len=len
    set "p2_div=%%i%%j"
    )
for /f "tokens=* delims=0" %%i in ("%p2_div%") do set /a p2_div=%%i
set /a divisor=p2_div,divisor_offset=p2_div_fd_len
set "int_quo="
set /a int_div_offset=divisor_offset
for /l %%i in (1,1,32) do (
    if !p1_int_div! lss %divisor% (
        set /a p1_int_div*=10,div_q=0
        set "int_quo=!int_quo!!div_q!"
        if %%i equ 1 (call :strlen "!div_q!"&set /a or_len=len)
        ) else (
        set /a div_q=!p1_int_div!/%divisor%,div_mod=!p1_int_div!%%%divisor%
        if %%i equ 1 (call :strlen "!div_q!"&set /a or_len=len)
        set "int_quo=!int_quo!!div_q!"
        set "p1_int_div=!div_mod!0"
        if !div_q! equ 0 goto :int_div_next
        )
    )
:int_div_next
set /a int_div_offset+=or_len
if %int_div_offset% gtr 0 (
for /f "tokens=* delims=0" %%i in ("!int_quo:~0,%int_div_offset%!") do if "%%i"=="" (set "int_quo_int=0") else set "int_quo_int=%%i"
set "int_quo_fd=!int_quo:~%int_div_offset%!"
) else (
for /l %%i in (-1,-1,%int_div_offset%) do set "int_quo=0!int_quo!"
set "int_quo_int=!int_quo:~0,1!"
set "int_quo_fd=!int_quo:~1!"
)
set "int_quo_result=%int_quo_int%.%int_quo_fd%"
set "fd_quo="
set /a dividend=p1_fd_div,fd_div_offset=divisor_offset-p1_fd_div_len-1
for /l %%i in (1,1,32) do (
    if !dividend! lss %divisor% (
        set /a dividend*=10,div_q=0
        set "fd_quo=!fd_quo!!div_q!"
        if %%i equ 1 (call :strlen "!div_q!"&set /a or_len=len)
        ) else (
        set /a div_q=!dividend!/%divisor%,div_mod=!dividend!%%%divisor%
        if %%i equ 1 (call :strlen "!div_q!"&set /a or_len=len)
        set "fd_quo=!fd_quo!!div_q!"
        set "dividend=!div_mod!0"
        if !div_mod! equ 0 goto :fd_div_next
        )
    )
:fd_div_next
set /a fd_div_offset+=or_len
if %fd_div_offset% gtr 0 (set /a fd_div_offset+=1)
if %fd_div_offset% gtr 0 (
for /f "tokens=* delims=0" %%i in ("!fd_quo:~0,%fd_div_offset%!") do if "%%i"=="" (set "fd_quo_int=0") else set "fd_quo_int=%%i"
set "fd_quo_fd=!fd_quo:~%fd_div_offset%!"
) else (
for /l %%i in (-1,-1,%fd_div_offset%) do set "fd_quo=0!fd_quo!"
set "fd_quo_int=!fd_quo:~0,1!"
set "fd_quo_fd=!fd_quo:~1!"
)
set "fd_quo_result=%fd_quo_int%.%fd_quo_fd%"
call :add "%int_quo_result%" "%fd_quo_result%"
endlocal&set "quo_result=%add_result%"
goto :eof
复制代码

用法：

R:\>byy.bat 202.3+1.029
203.329

R:\>byy.bat 202.3*1.029
208.16669997223652899265289306640625

R:\>byy.bat 20231102.1102
4497.8997651170000000000000000000000

R:\>byy.bat 2023.1102/1102
1.8358531760435571687840290381125
复制代码

buyiyang

第二部分

:sqrt
for /f "tokens=1-2 delims=." %%i in ("%~1") do (
    set "p1_int_sqrt=%%i"
    if "%%j"=="" (set /a p1_fd_sqrt=0) else set "p1_fd_sqrt=%%j"
    )
call :int2bin "%p1_int_sqrt%"
set "p1_int_sqrt_bin=%int_bin%"
call :fd2bin "%p1_fd_sqrt%"
set "p1_fd_sqrt_bin=%fd_bin%"
set "p1_sqrt_bin=%p1_int_sqrt_bin%%p1_fd_sqrt_bin%"
call :strlen "%p1_sqrt_bin%"&set /a before=len
for /f "tokens=* delims=0" %%i in ("%p1_sqrt_bin%") do set "p1_sqrt_bin=%%i"&call :strlen "%%i"
set /a zero_offset=len-before
call :strlen "!p1_int_sqrt_bin!"
set /a p1_sqrt_offset=len-1+zero_offset,e_de=127+p1_sqrt_offset
call ::int2bin "%e_de%"
set "e_bin=%int_bin%"
set "zero_fill="
for /l %%i in (1,1,8) do set "zero_fill=!zero_fill!0"
set "e_bin=%zero_fill%%e_bin%"
set "e_bin=%e_bin:~-8%"
set "m=%p1_sqrt_bin:~1%"
set "m=%m:~0,23%"
set "p1_ieee=0%e_bin%%m%"
rem echo,%p1_ieee%
call :sub_bin "1011111001101110101101010000110" "0%p1_ieee:~0,-1%"
call :bin2dec "%sub_bin_result:~1,8%"
set /a sub_bin_result_offset=int_sum-127
set "sub_bin_result_m=1%sub_bin_result:~-23%"
if %sub_bin_result_offset% gtr 0 (set /a sub_bin_result_offset+=1)
if %sub_bin_result_offset% gtr 0 (
set "sub_bin_result_int=!sub_bin_result_m:~0,%sub_bin_result_offset%!"
set "sub_bin_result_fd=!sub_bin_result_m:~%sub_bin_result_offset%!"
) else (
for /l %%i in (-1,-1,%sub_bin_result_offset%) do set "sub_bin_result_m=0!sub_bin_result_m!"
set "sub_bin_result_int=!sub_bin_result_m:~0,1!"
set "sub_bin_result_fd=!sub_bin_result_m:~1!"
)
call :bin2dec "%sub_bin_result_int%" "%sub_bin_result_fd%"
set "sqrt_result1=%bin2dec_result%"
call :div "1" "%sqrt_result1:~0,9%"
set "sqrt_result0=%quo_result%"
rem echo,%sqrt_result0%
for /f "tokens=1-2 delims=." %%i in ("%sqrt_result0%") do set "j=%%j"&set "sqrt_result0=%%i.!j:~0,9!"
call :div "%sqrt_result0%" "2"
set "x=%quo_result%"
call :add "%~1" "0"
for /f "tokens=1-2 delims=." %%i in ("%add_result%") do set "j=%%j"&set "pre_y=%%i.!j:~0,9!"
call :div "%pre_y%" "%sqrt_result0:~0,9%"
for /f "tokens=1-2 delims=." %%i in ("%quo_result%") do set "j=%%j"&set "y=%%i.!j:~0,9!"
call :div "%y%" "2"
set "y=%quo_result%"
call :add "%x%" "%y%"
set "sqrt_result00=%add_result%"
for /f "tokens=1-2 delims=." %%i in ("%sqrt_result00%") do set "j=%%j"&set "sqrt_result00=%%i.!j:~0,9!"
call :div "%sqrt_result00%" "2"
set "x=%quo_result%"
call :add "%~1" "0"
for /f "tokens=1-2 delims=." %%i in ("%add_result%") do set "j=%%j"&set "pre_y=%%i.!j:~0,9!"
call :div "%pre_y%" "%sqrt_result00:~0,9%"
for /f "tokens=1-2 delims=." %%i in ("%quo_result%") do set "j=%%j"&set "y=%%i.!j:~0,9!"
call :div "%y%" "2"
set "y=%quo_result%"
call :add "%x%" "%y%"
set "sqrt_result=%add_result%"
goto :eof

:strlen
set "s=%~1"
set "zz=0 1 2 3 4 5 6 7 8 9 a b c d e f"
if not defined list for %%a in (%zz%)do for %%b in (%zz%)do set list=!list!%%a%%b
set "s=!list!!s!!s!"
set /a len=0X%s:~-512,2%
goto :eof

:int2bin
set /a i=%~1
set "int_bin="
if %i% gtr 0 (set /a s=0) else if %i% lss 0 (set /a s=1,i=-i) else (set /a int_bin=0,s=0&goto :eof)
for /l %%i in (1,1,32) do if !i! neq 1 (
    set /a ii=i,i=i/2,bin=ii%%2
    set int_bin=!bin!!int_bin!) else (
    set int_bin=1!int_bin!
    goto :eof
    )
goto :eof

:fd2bin
if %~1 equ 0 (
    set "zero_fill="
    for /l %%i in (1,1,32) do set "zero_fill=!zero_fill!0"
    set "fd_bin=!zero_fill!"
    goto :eof
    )
set "fd_bin="
set "f=0.%~1"
for /l %%i in (1,1,32) do (
    call :add "!f!" "!f!"
    if !int_dec! geq 1 (set fd_bin=!fd_bin!1) else set fd_bin=!fd_bin!0
    set "f=0.!fd_dec!"
    )
goto :eof

:add_bin
set "p1_bin=%~1"
set "p2_bin=%~2"
set "bin_result="
set /a carry=0
call :strlen "%p1_bin%"
set /a p1_bin_len=%len%
call :strlen "%p2_bin%"
set /a p2_bin_len=%len%
if %p1_bin_len% geq %p2_bin_len% (set /a bin_len_max=p1_bin_len+1) else set /a bin_len_max=p2_bin_len+1
for /l %%i in (-1,-1,-%bin_len_max%) do (
    if %%i lss -%p1_bin_len% (set /a p1_bin_place=0) else set "p1_bin_place=!p1_bin:~%%i,1!"
    if %%i lss -%p2_bin_len% (set /a p2_bin_place=0) else set "p2_bin_place=!p2_bin:~%%i,1!"
    set /a bin_place=!p1_bin_place!+!p2_bin_place!+!carry!
    if !bin_place! geq 2 (set /a carry=bin_place/2,bin_place=bin_place-2) else set /a carry=0
    set "bin_result=!bin_place!!bin_result!"
    )
set "add_bin_result=%bin_result%"
goto :eof

:bin2dec
set "int_bin=%~1"
set "fd_bin=%~2"
set /a int_sum=0
if "%~1"=="" goto :fd_bin2dec
call :strlen "%int_bin%"
set /a int_len=len
set /a bin2dec_n=1,int_sum=0
for /l %%i in (-1,-1,-%int_len%) do (
    if "!int_bin:~%%i,1!"=="1" (
        call :add "!int_sum!" "!bin2dec_n!"
        set "int_sum=!add_result!"
        )
    call :add "!bin2dec_n!" "!bin2dec_n!"
    set "bin2dec_n=!add_result!"
    )
if "%~2"=="" goto :eof
:fd_bin2dec
set "bin2dec_half=0.5"
set /a fd_sum=0
for /l %%i in (0,1,32) do if not "!fd_bin:~%%i,1!"=="" (
    if "!fd_bin:~%%i,1!"=="1" (
        call :add "!fd_sum!" "!bin2dec_half!"
        set "fd_sum=!add_result!"
        )
    call :fd_half "!bin2dec_half!"
    set "bin2dec_half=!fd_half!"
    )
call :add "%int_sum%" "%fd_sum%"
set "bin2dec_result=%add_result%"
goto :eof

:sub_bin
set "sub_bin_p1=%~1"
set "sub_bin_p2=%~2"
set "sub_bin_result="
set /a sub_bin_carry=0
for /l %%i in (-1,-1,-32) do (
    set /a sub_bin_p1_place=!sub_bin_p1:~%%i,1!+sub_bin_carry
    set "sub_bin_p2_place=!sub_bin_p2:~%%i,1!"
    if !sub_bin_p1_place! lss !sub_bin_p2_place! (set /a sub_bin_p1_place+=2,sub_bin_carry=-1
    ) else set /a sub_bin_carry=0
    set /a diffe=sub_bin_p1_place-sub_bin_p2_place
    set "sub_bin_result=!diffe!!sub_bin_result!"
    )
goto :eof

:fd_half
set "fd_half="
set "one=%~1"
set "one=%one:*.=%"
for /l %%i in (0,1,32) do (
    if "!one:~%%i,1!"=="" (set "one_i=!pre!0") else set "one_i=!pre!!one:~%%i,1!"
    set /a one_ii=one_i,one_i=one_i/2,one_mod=one_ii%%2
    if "!one_mod!"=="0" (set "pre=") else set /a pre=one_mod
    set "fd_half=!fd_half!!one_i!"
    if "!one:~%%i,1!"=="" (if "!one_mod!"=="0" goto :fd_half_next)
    )
:fd_half_next
set "fd_half=0.%fd_half%"
goto :eof
复制代码

Batcher

这里有几个浮点数计算的代码，感兴趣的朋友们可以一起看看：
http://bbs.bathome.net/thread-3322-1-1.html
http://bbs.bathome.net/thread-3372-1-1.html