[数值计算] 批处理如何更准确地计算e的值？

chineseman2

setlocal delayexpansion
set a=1
set b=1
set c=10000000
@echo off
@cls
:loop
set /a c=c+(10000000/b)
set /a a=a+1
set /a b=b*a
if %a% equ 500 goto :ex
goto :loop
:ex
set /a c=c-20000000
@echo E is 2.%c%
@echo off
@pause>nul
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e本来等于2.718281828...
但是它只给出e=2.7182814和一大堆Divide by zero error.
如何更准确地计算e？（bat计算...)

terse

再简化一行
一处笔误  貌似没变化

@echo off&setlocal enabledelayedexpansion
set lp=100
set /a A=10000,M=1000
set/aLp=(Lp+3)/4*14
for /l %%i in (%LP% -1 1) do set/a "S+=M*A,R_%%i=S%%%%i,S/=%%i"
   set /a "E=S/A+M,M=S%%A,Lp-=14"
   set _E=%_E%%E:~,4%
   for /l %%i in (!Lp! -14 1) do (
       for /l %%j in (%%i -1 1) do set/a "S+=R_%%j*A,R_%%j=S%%%%j,S/=%%j"
       set /a "E=S/A+M,M=S%%A+A"
       set _E=!_E!!E:~-4!
   )
)
echo;!_E!
pause
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batman

批无法直接计算浮点同时cmd只能计算2^31内的值(-2147483648-2147483647)，用VBS计算循环到171次也就是b=171!时溢出：

Dim a, b, c
b = 1 : c = 10000000
For i = 1 To 500
  On Error Resume Next
  a = a + 1
  b = b * a
  c = c + 10000000 / b
  If Num = "" And Err.Number <> 0 Then Num = i 
  Err.Clear
Next
c = c - 20000000
WScript.Echo "E=2." & c & vbCrLf & Num
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chineseman2

http://zh.wikipedia.org/wiki/E_(%E6%95%B0%E5%AD%A6%E5%B8%B8%E6%95%B0)