Erlang整数的平方根

    使用切线法实现了求整数的平方根. 对于10000位的整数计算耗时仅140ms, 应该说速度还可以. 算法实现关键有两点: (1) 初始值的估算; (2) 算法的终止条件. 有兴趣的朋友看代码时注意这两点就可以了. 算法耗时部分已用红色标注.

 

-module(mymath).
-compile(export_all).

%求整数的平方根, 整数I的平方根是X, 满足 K*K =< I =< (K+1)*(K+1)
%@spec isqrt(integer()) -> integer()
%使用了切线法, 不过对初值进行了粗略估算, 大大加快了运算速度
isqrt(I) when is_integer(I)  ->
    Len =length(integer_to_list(I)),
    case (Len rem 2) of
        0 -> isqrt1(I,ipow10( Len div 2));
        1 -> isqrt1(I,ipow10( Len div 2 +1))
    end.

isqrt1(I,X) ->
    NextX = (I div X + X) div 2,
    if
        NextX>=X -> X;
        true -> isqrt1(I, NextX)
    end.
%10的非负整数次幂
%@spec ipow10( integer() ) -> integer()
ipow10(N) when N>=0, is_integer(N) -> ipow10(N,[]).
ipow10(N,L) ->
    if
        N==0 -> list_to_integer([49|L]);
        true -> ipow10(N-1,[48|L])
    end.
    

1> c(mymath.erl).
{ok,mymath}
2> I=mymath:ipow10(10000).
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0
3> {T,R}=timer:tc(mymath,isqrt,[I+I]).
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4> T.
140000
5>