China DOS Union

The algorithm idea was proposed by terse. I expanded the feasible range.

@echo off set /p n=Enter the number to be square-rooted (0~89999999): set a=2 :acr set /a a=(n/a+a)/2,b=a*a if %b% gtr %n% goto :acr if %b% lss 0 goto acr if %b% equ %n% goto :ok set /a t=n-b,k=a :loop1 set /a t*=100,x=k*20,m=10 :loop2 set /a m-=1,s=m*(m+x) if %s% gtr %t% goto loop2 set /a t-=s,c+=1,k=k*10+m,r=r*10+m if %c% lss 5 goto loop1 :ok if not "%r%" == "" set a=%a%.%r% echo Result: %a% pause>nul

[ Last edited by dreamseed on 2008-4-5 at 05:13 PM ]

() - grouping
! ~ - - unary operators
* / % - arithmetic operators
+ - - arithmetic operators
<< >> - logical shifts
- bitwise "and"
^ - bitwise "xor"
| - bitwise "or"
= *= /= %= += -= - assignment
&= ^= |= <<= >>=
, - expression separator

Make use of logical operators

Can you write out a concrete example?

Using batch files for math calculations, especially decimals, I really haven't studied that before,

Threads like this are just for fun, and can be kept around as a small utility function,

Let's study the algorithm
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It's purely a computational mathematics problem, mainly the iterative formula: Xn+1=(Xn+A/Xn)/2 limit----->A^(1/2)

At the start, the OP sets X1 to 2, then in the :acr module iteratively computes the integer part of A^(1/2),

if %b% lss 0 goto acr is not redundant; it's there to prevent overflow into a negative number. I overlooked that

Also, setting X1 to n/2 can reduce the number of iterations,

As for the decimal part afterward, someone else can analyze it, I don't have the patience anymore

[ Last edited by plp626 on 2008-4-5 at 06:46 PM ]

Let the next person take a look, thanks.