问题
I was just wondering what different strategies there are for division when dealing with big numbers. By big numbers, I mean ~50 digit numbers .
e.g. 9237639100273856744937827364095876289200667937278 / 8263744826271827396629934467882946252671
When both numbers are big, long division seems to lose its usefulness...
I thought one possibility is to count through multiplications of the divisor until you go over the dividend, but if it was the dividend in the example above divided by a small number, e.g. 4, then that's a huge amount of calculations to do.
So, is there simple, clean way to do this?
回答1:
What language / platform do you use? This is most likely already solved, so you don't need to implement it from scratch. E.g. Haskell has the Integer type, Java the java.math.BigInteger class, .NET the System.Numerics.BigInteger structure, etc.
If your question is really a theoretical one, I suggest you read Knuth, The Art of Computer Programming, Volume 2, Section 4.3.1. What you are looking for is called "Algorithm D" there. Here is a C implementation of that algorithm along with a short explanation: http://hackers-delight.org.ua/059.htm
回答2:
Long division is not very complicated if you are working with binary representations of your numbers and probably the most efficient algorithm.
回答3:
if you don't need very exact result, you can use logarithms and exponents.
Exponent is the function f(x)=e^x, where e is a mathmaticall constant equal to 2.71828182845...
Logarithm (marked by ln) is the inverse of the exponent.
Since ln(a/b)=ln(a)-ln(b), to calculate a/b you need to:
Calculate ln(a) and ln(b) [By library function, logarithm table or other methods]
substruct them: temp=ln(a)-lb(b)
calculate the exponent e^temp
来源：https://stackoverflow.com/questions/12233968/division-with-really-big-numbers