Огромные числа в java

Immutable arbitrary-precision integers. All operations behave as if BigIntegers were represented in two’s-complement notation (like Java’s primitive integer types). BigInteger provides analogues to all of Java’s primitive integer operators, and all relevant methods from java.lang.Math. Additionally, BigInteger provides operations for modular arithmetic, GCD calculation, primality testing, prime generation, bit manipulation, and a few other miscellaneous operations. Semantics of arithmetic operations exactly mimic those of Java’s integer arithmetic operators, as defined in The Java™ Language Specification. For example, division by zero throws an ArithmeticException , and division of a negative by a positive yields a negative (or zero) remainder. Semantics of shift operations extend those of Java’s shift operators to allow for negative shift distances. A right-shift with a negative shift distance results in a left shift, and vice-versa. The unsigned right shift operator ( >>> ) is omitted since this operation only makes sense for a fixed sized word and not for a representation conceptually having an infinite number of leading virtual sign bits. Semantics of bitwise logical operations exactly mimic those of Java’s bitwise integer operators. The binary operators ( and , or , xor ) implicitly perform sign extension on the shorter of the two operands prior to performing the operation. Comparison operations perform signed integer comparisons, analogous to those performed by Java’s relational and equality operators. Modular arithmetic operations are provided to compute residues, perform exponentiation, and compute multiplicative inverses. These methods always return a non-negative result, between 0 and (modulus — 1) , inclusive. Bit operations operate on a single bit of the two’s-complement representation of their operand. If necessary, the operand is sign- extended so that it contains the designated bit. None of the single-bit operations can produce a BigInteger with a different sign from the BigInteger being operated on, as they affect only a single bit, and the arbitrarily large abstraction provided by this class ensures that conceptually there are infinitely many «virtual sign bits» preceding each BigInteger. For the sake of brevity and clarity, pseudo-code is used throughout the descriptions of BigInteger methods. The pseudo-code expression (i + j) is shorthand for «a BigInteger whose value is that of the BigInteger i plus that of the BigInteger j .» The pseudo-code expression (i == j) is shorthand for » true if and only if the BigInteger i represents the same value as the BigInteger j .» Other pseudo-code expressions are interpreted similarly. All methods and constructors in this class throw NullPointerException when passed a null object reference for any input parameter. BigInteger must support values in the range -2 Integer.MAX_VALUE (exclusive) to +2 Integer.MAX_VALUE (exclusive) and may support values outside of that range. An ArithmeticException is thrown when a BigInteger constructor or method would generate a value outside of the supported range. The range of probable prime values is limited and may be less than the full supported positive range of BigInteger . The range must be at least 1 to 2 500000000 .

Field Summary

Constructor Summary

Translates a byte array containing the two’s-complement binary representation of a BigInteger into a BigInteger.

Translates a byte sub-array containing the two’s-complement binary representation of a BigInteger into a BigInteger.

Constructs a randomly generated positive BigInteger that is probably prime, with the specified bitLength.

Constructs a randomly generated BigInteger, uniformly distributed over the range 0 to (2 numBits — 1), inclusive.

Method Summary

Returns the number of bits in the two’s complement representation of this BigInteger that differ from its sign bit.

Returns the number of bits in the minimal two’s-complement representation of this BigInteger, excluding a sign bit.

Returns the index of the rightmost (lowest-order) one bit in this BigInteger (the number of zero bits to the right of the rightmost one bit).

Returns an array of two BigIntegers containing the integer square root s of this and its remainder this — s*s , respectively.

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Class BigInteger

Semantics of arithmetic operations exactly mimic those of Java’s integer arithmetic operators, as defined in The Java Language Specification. For example, division by zero throws an ArithmeticException , and division of a negative by a positive yields a negative (or zero) remainder.

Semantics of shift operations extend those of Java’s shift operators to allow for negative shift distances. A right-shift with a negative shift distance results in a left shift, and vice-versa. The unsigned right shift operator ( >>> ) is omitted since this operation only makes sense for a fixed sized word and not for a representation conceptually having an infinite number of leading virtual sign bits.

Semantics of bitwise logical operations exactly mimic those of Java’s bitwise integer operators. The binary operators ( and , or , xor ) implicitly perform sign extension on the shorter of the two operands prior to performing the operation.

Comparison operations perform signed integer comparisons, analogous to those performed by Java’s relational and equality operators.

Modular arithmetic operations are provided to compute residues, perform exponentiation, and compute multiplicative inverses. These methods always return a non-negative result, between 0 and (modulus — 1) , inclusive.

Bit operations operate on a single bit of the two’s-complement representation of their operand. If necessary, the operand is sign-extended so that it contains the designated bit. None of the single-bit operations can produce a BigInteger with a different sign from the BigInteger being operated on, as they affect only a single bit, and the arbitrarily large abstraction provided by this class ensures that conceptually there are infinitely many «virtual sign bits» preceding each BigInteger.

For the sake of brevity and clarity, pseudo-code is used throughout the descriptions of BigInteger methods. The pseudo-code expression (i + j) is shorthand for «a BigInteger whose value is that of the BigInteger i plus that of the BigInteger j .» The pseudo-code expression (i == j) is shorthand for » true if and only if the BigInteger i represents the same value as the BigInteger j .» Other pseudo-code expressions are interpreted similarly.

All methods and constructors in this class throw NullPointerException when passed a null object reference for any input parameter. BigInteger must support values in the range -2 Integer.MAX_VALUE (exclusive) to +2 Integer.MAX_VALUE (exclusive) and may support values outside of that range. An ArithmeticException is thrown when a BigInteger constructor or method would generate a value outside of the supported range. The range of probable prime values is limited and may be less than the full supported positive range of BigInteger . The range must be at least 1 to 2 500000000 .

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Class BigInteger

Comparison operations perform signed integer comparisons, analogous to those performed by Java’s relational and equality operators.

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Large Numbers in Java

How would I go about doing calculations with extremely large numbers in Java? I have tried long but that maxes out at 9223372036854775807, and when using an integer it does not save enough digits and therefore is not accurate enough for what I need. Is there anyway around this?

6 Answers 6

You can use the BigInteger class for integers and BigDecimal for numbers with decimal digits. Both classes are defined in java.math package.

BigInteger reallyBig = new BigInteger("1234567890123456890"); BigInteger notSoBig = new BigInteger("2743561234"); reallyBig = reallyBig.add(notSoBig);

Might be worth mentioning the (though obvious for most, I guess) inherit performance hit incurred by the use of the BigInteger class if you plan to do calculations with that.

@haylem the performance speed is the same but the length of the number makes it takes time. they use bitwise operators to do the calculations. like what happens normally when doing math with primitive types.

Use the BigInteger class that is a part of the Java library.

Here is an example which gets big numbers very quickly.

import java.math.BigInteger; /* 250000th fib # is: 36356117010939561826426 . 10243516470957309231046875 Time to compute: 3.5 seconds. 1000000th fib # is: 1953282128707757731632 . 93411568996526838242546875 Time to compute: 58.1 seconds. */ public class Main < public static void main(String. args) < int place = args.length >0 ? Integer.parseInt(args[0]) : 250 * 1000; long start = System.nanoTime(); BigInteger fibNumber = fib(place); long time = System.nanoTime() - start; System.out.println(place + "th fib # is: " + fibNumber); System.out.printf("Time to compute: %5.1f seconds.%n", time / 1.0e9); > private static BigInteger fib(int place) < BigInteger a = new BigInteger("0"); BigInteger b = new BigInteger("1"); while (place-- >1) < BigInteger t = b; b = a.add(b); a = t; >return b; > >

For really large Fibonacci numbers, the recursive calculation is ridiculously time consuming. Much better to use Binet’s explicit formula. A few Math.pow()s and Math.sqrt()s later, you’re done! 🙂

@ZubinMukerjee however pow and sqrt on BigDecimal isn’t cheap either. It is better than iteration but not as simple as it sounds.

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