I have to solve a problem in java which has an input consisting of 10^100 digits.
How can I take such a large input and process it.I am using JAVA as my programming language.
Are all those digits actually significant? Or do you just have a value like 1.234567890123456789 * 10^100?
As others have noted, having 10^100 essential digits would essentially mean you can stop now and write off your problem as uncomputable. You've either misunderstood it, or you shouldn't be approching it via brute-force number crunching. Or both.
If you don't need all the lower-order digits, then floats or doubles may do the job for you. If you need more digits of precision than a double can handle (but still a REASONABLE number), an extended-precision floating point package such as BigFloat might get you there.
If you told us what you were actually trying to do, we could tell you more about whether there's any reasonable way to do it.
Related
I was wondering how to replace common trigonometric values in an expression. To put this into more context, I am making a calculator that needs to be able to evaluate user inputs such as "sin(Math.PI)", or "sin(6 * math.PI/2)". The problem is that floating point values aren't accurate and when I input sin(Math.PI), the calculator ends up with:
1.2245457991473532E-16
But I want it to return 0. I know I could try replacing in the expression all sin(Math.PI) and other common expressions with 0, 1, etc., except I have to check all multiples of Math.PI/2. Can any of you give me some guidance on how to return the user the proper values?
You're running into the problem that it's not quite possible to express a number like pi in a fixed number of bits, so with the available machine precision the computation gives you a small but non-zero number. Math.PI in any case is only an approximation of PI, which is an irrational number. To clean up your answer for display purposes, one possibility is to use rounding. You could instead try adding +1 and -1 to it which may well round the answer to zero.
This question here may help you further:
Java Strange Behavior with Sin and ToRadians
Your problem is that 1.2245457991473532E-16 is in fact zero for many purposes. What about simply rounding the result yielded by sin? With enough rounding, you may achieve what you want and even get 0.5, -0.5 and other important sin values relatively easily.
If you really want to replace those functions as your title suggests, then you can't do that in Java. Your best bet would be to create an SPI specification for common functions that could either fall back to the standard Java implementation or use your own implementation, which replaces the Java one.
Then users of your solution would need to retrieve one of the implementations using dependency injection of explicit references to a factory method.
Well I am working on a big dataset and after some calculations I am getting values for the features like 4.4E-5. I read it somewhere those values means 0.000044 that is ten to the power minus 5. So my question is whenever I want to use them for further processing will these values behave same as float works or do I need some other data type?
Yes, it is an extended notation presenting the same binary floating point data type.
Both 4.4E-5 and 0.00044 are the same. And that value only approximates 0.000044 with a sum of powers of 2: 2^-18 + ...
Multiplying lots of small numbers leads to underflow. Take the log and add. This technique is universal in computer science. Many of the Google hits for "underflow log" are useful, including SO hits, other techniques for dealing with it, etc.
For a Java assignment I am required to be able to pass any number that will be introduced as a string through the command line (no matter how big) into binary.
Then generate methods that will allow these numbers to add, multiply, subtract and divide.
My question would be first:
How do I make my string into binary
Eg:
123 would become 1111011
8403678 would become 100000000011101011011110
And so forth...
Then the biggest issue is to get them to add up, subtract each other, etc.
Last I need to be able to convert back the result from binary back to decimal which I am having more trouble understanding how to do it than the previous case (transforming from binary into a decimal string).
Eg:
if 1111011 was added to 100000000011101011011110 the result would be 100000000011101101011001 and then it would become 8403801 which I would print out as a result.
The final aim of this project is to create our own class such as java.math.BigInteger (without using it of course) and handling arbitrarily big numbers (bigger than what Int can handle).
If there is any extra information required please let me know I will answer promptly.
Since you have to be able to handle large numbers without using BigInteger, you need to find a way to represent arbitrarily large numbers. Obviously int will not do. One easy way is to represent the number as a String. For instance, the number 123 could be stored as the String "123".
Converting to binary will require some intermediate operations such as division and modulo. Thus, it is worth thinking about how to do these when your numbers are stored in Strings. Since this is homework I don't want to just give you the answer, but some guidance instead.
Say you want to do addition.
Think about how you add big numbers by hand. Which digits of each number do you use, and how do you manipulate them to get the answer? This algorithm is fairly straightforward, and once you can explain it, you can give a computer directions to do it as well. (For addition, you add first the one's digits, then the ten's digits, etc... and remember to carry if you have to!)
Note that you can get the digits of your number String by using a method such as charAt(int n). This will return the character at index n of the string. Convert it to an Integer by using Integer.parseInt() (which takes a numeric string and converts it to an integer).
So now you can think: If I want the one's digit of a number, what index would that be in a String? Starting with this, you should be able to figure out how to get any digit you want from a big number string. Now, you can implement your algorithm.
Finally, to convert from base ten to binary you do need to understand how number bases work. This gives a clear and quick introduction: http://www.math.grin.edu/~rebelsky/Courses/152/97F/Readings/student-binary
The section "Converting from decimal to binary" in the above link describes a method for exactly what you want to do. Good luck.
I have an assignment (i think a pretty common one) where the goal is to develop a LargeInteger class that can do calculations with.. very large integers.
I am obviously not allowed to use the Java.math.bigeinteger class at all.
Right off the top I am stuck. I need to take 2 Strings from the user (the long digits) and then I will be using these strings to perform the various calculation methods (add, divide, multiply etc.)
Can anyone explain to me the theory behind how this is supposed to work? After I take the string from the user (since it is too large to store in int) am I supposed to break it up maybe into 10 digit blocks of long numbers (I think 10 is the max long maybe 9?)
any help is appreciated.
First off, think about what a convenient data structure to store the number would be. Think about how you would store an N digit number into an int[] array.
Now let's take addition for example. How would you go about adding two N digit numbers?
Using our grade-school addition, first we look at the least significant digit (in standard notation, this would be the right-most digit) of both numbers. Then add them up.
So if the right-most digits were 7 and 8, we would obtain 15. Take the right-most digit of this result (5) and that's the least significant digit of the answer. The 1 is carried over to the next calculation. So now we look at the 2nd least significant digit and add those together along with the carry (if there is no carry, it is 0). And repeat until there are no digits left to add.
The basic idea is to translate how you add, multiply, etc by hand into code when the numbers are stored in some data structure.
I'll give you a few pointers as to what I might do with a similar task, but let you figure out the details.
Look at how addition is done from simple electronic adder circuits. Specifically, they use small blocks of addition combined together. These principals will help. Specifically, you can add the blocks, just remember to carry over from one block to the next.
Your idea of breaking it up into smaller blogs is an excellent one. Just remember to to the correct conversions. I suspect 9 digits is just about right, for the purpose of carry overs, etc.
These tasks will help you with addition and subtraction. Multiplication and Division are a bit trickier, but again, a few tips.
Multiplication is the easier of the tasks, just remember to multiply each block of one number with the other, and carry the zeros.
Integer division could basically be approached like long division, only using whole blocks at a time.
I've never actually build such a class, so hopefully there will be something in here you can use.
Look at the source code for MPI 1.8.6 by Michael Bromberger (a C library). It uses a simple data structure for bignums and simple algorithms. It's C, not Java, but straightforward.
Its division performs poorly (and results in slow conversion of very large bignums to tex), but you can follow the code.
There is a function mpi_read_radix to read a number in an arbitrary radix (up to base 36, where the letter Z is 35) with an optional leading +/- sign, and produce a bignum.
I recently chose that code for a programming language interpreter because although it is not the fastest performer out there, nor the most complete, it is very hackable. I've been able to rewrite the square root myself to a faster version, fix some coding bugs affecting a port to 64 bit digits, and add some missing operations that I needed. Plus the licensing is BSD compatible.
Im facing a scenario where in ill have to compute some huge math expressions. The expressions in themselves are simple, ie have just the conventional BODMAS fundamental but the numbers that occur as operands are very large, to the tune of 1000 digit numbers. I do know of the BigInteger class of the java.math module but am looking for a different way so that the computation can occur also in a speedy manner. Im a guy still finding his feet in Java, so any pointers or advice in gthis regard would be of great help.
Regards
p1nG
Try it with BigInteger, profile the results with some test calculations, and see if it will work for you, before you look for something more optimized.
Since you say you are new to Java, I would have to suggest you use BigInteger and BigDecimal unless you want to write your own arbitrarily large number handlers. BigInteger and BigDecimal are fast enough for most uses of them. The only time I've had speed issues with them is when dealing with numbers on the order of a million digits.
That is unless you have a specific need for not using BigInteger.
First write the program correctly (using BigFoo) and then determine if optimization is appropriate.
BigInteger/BigFloat will be the most optimized implementation of generalized math that you will possibly get.
If you want it faster, you MIGHT be able to write assembly to use bit-shifting patters for specialized math (well, like divide by 2 tends to be a simple right shift), but if you are doing more than a few different types of equations, that will be very impractical.
BigInteger is only slow in comparison to int, but it will probably be the best you are going to possibly get for operations on numbers of more than 64 bits or so without going to another language--and even then you probably won't get much of an improvement unless that other language is assembly...
I am surprised that equations with 1000 digits have a practical application (except perhaps encryption)
Could you could explain what you are doing and what your speed requirements are?