RE: Slowness in bignum mode ( gmp | gawk -M ) when doubling extremely large inputs

[pjfarley3]

As an exercise for myself, I manually reformatted this _2x_ function converting 
the "all underscore" names to names like _n1, _n2, etc. up to _n12 to make the 
code a little easier to understand.

It would have been more helpful if the variable names had been chosen for what 
function / intermediate result they represent rather than just arbitrary names. 
Or the names could just have been any sequence of single-letter variable names 
for more brevity.

Using absolutely minimal spacing everywhere reduces the byte space occupied but 
is much harder for humans unfamiliar with the algorithm to understand.

Embedding assignments in "if" conditions may be optimal, but IMHO make the code 
much harder to understand, especially with minimal spacing as well.

There are also several strange uses of the exclamation point operator (!) that 
I do not understand, but that is probably just my lack of experience.  Examples 
of such use are:

_n1-!!_n1
-!-""
!+""
!--_n10

I THINK these are intended to be uses of the negation operator, but I don’t 
understand what that operation is supposed to do to an empty string.

Reformatted results are pasted below.  Corrections welcomed, if you are 
interested.  I may also run this copy through a pretty-printer to see what that 
looks like.

Peter

Reformatted function _2x_:

function _2x_(_n2,_n1,_n7,_n4,_n9,
    _n11,_n10,_n12,_n8,_n5,_n6,_n3) {
    if(_n2!~/[1-9]/) {
        return +_n1
    }
    _n3=(_n2~/^[-]/)
    sub("^[+-]?["(-"")"]*","",_n2)
    if (length(_n2)<(_n5=((_n1+=++_n1)^_n1^_n1-!!_n1))+_n1) {
        if (_n9^((_n5+(_n1~_n4))^(_n5-_n1)<+_n2)) {
            return (-!-"")^_n3*(+_n2+_n2)
        }
    }
    _n3=substr("-",_n1~"",_n3)
    if (_n2!~"[5-9]") {
        gsub(/4/,"8",_n2)-gsub(/3/,"6",_n2)
        gsub(/2/,"4",_n2)-gsub(/1/,"2",_n2)
        return (_n3)_n2
    };
    _n7=_n4=_n8="";
    _n2=(_n5=substr(_n8=(_n1++^_n1--+_n1)^_n5,_n1))(_n2)
    gsub(/./,".",_n5)
    sub("("(_n5)")+$","_&",_n2)
    _n2=substr(_n2,index(_n2,"_")+!+"")
    _n8+=+_n8;_n1="";
    if ((gsub(_n5,"&_",_n2)+gsub(/[_n1][5-9]/,".5&",_n2)*(+""))%2) {
        _n1=(":")(_n8+_n2+_n2)
        _n2=substr(_n2,index(_n2,"_")+!+"")
    }
    for(_n5 in _n6) { }
    if (_n6[_n5=split(_n2,_n6,/[_n1]/)]=="") {
        delete _n6[_n5--]
    };
    _n2=_n4~_n4;
    _n10=_n12*=\
        _n12=_n11=_n9=32;
    while(_n2<_n5) { 
        if(!--_n10){
            _n10=_n12;_n7=(_n7)_n1;
            _n1="";
            if(!--_n11){
                _n11=_n9;_n4=(_n4)_n7;_n7="";
            }
        }
        _n1=(_n1)(":")(+_n6[_n2++]*2+_n8)\
            (":")(+_n6[_n2++]*2+_n8)
    }
    _n4=(_n4)(_n7)(_n1)\
        (_n2==_n5?(":")(_n8+2*_n6[_n5]):"")
    gsub(/[:]+[^:]/,"",_n4)
    sub(/^0*/,"",_n4); 
    return (_n3)_n4 
}