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MegaMath is a small, handy C#/VB .Net library designed to compute basic math functions on extremely large integers represented as strings.






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This article is a follow-up to How to do a multiplicative inverse of an extremely large integer using System.Numerics.BigInteger. This post details a technique to reduce the memory required to store and multiply mega-digits by a given number. In the post, we explain the efficiency of certain algorithms when dealing with large integers. Using the Numerics.BigInteger type, we can store and multiply arbitrarily large integers. The BigInteger structure uses 96 bits to store an integer. The.NET Framework uses 32 bits to store an integer, which means that you can only store 1,048,576 (2^32) items in a BigInteger object. Storing megadigits requires more memory than storing gigadigits. But, this cost can be amortized over many calculations. In this article, we use the function IsEven(a) to determine whether a is an even or odd number. Using a modulus operator, the function returns true if a % 2 == 0, false otherwise. The function is a good general-purpose test for any value. To find the nth power of any base, you can do this using this code: The trick is to get n as a string of decimal digits. This is done by using a format specifier. For example: 123456789012345678901234567890 1.234567890123456789012345678901 Output: 1234567890123456789012345678901 The nth power of a number is computed as: x^n = (x * x * x... x) ^ n Some examples: 1^2 = 2^1 = 1 1^3 = 2^2 = 4 1^4 = 2^3 = 8 1^5 = 2^4 = 16 1^6 = 2^5 = 32 1^7 = 2^6 = 64 ... 1^20 = 2^12 = 1024 1^21 = 2^13 = 1024 Using the function Power(x, n), you can get a value close to the nth power of a number. This has advantages over simply using exponents because it works for non-integers. The alg



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--------------------------------- Multimillicent Math library, implemented in C#. Multi-multimillicent. It is a fairly large library. Contains more than 80 functions that perform basic math functions. Version: 1.0: Initial Release. 1.0.4: Fixed an issue with the Int64 type that was causing a double exception. Added a RegressionTest. 1.1: Added Math.Abs(Int64). Added Math.Ceiling(Int64). Added Math.Pow(Int64, Int64). Added Math.Round(Int64, Int32, Int32). Added Math.Truncate(Int64, Int32, Int32). Added Math.Abs(Double). Added Math.Ceiling(Double). Added Math.Pow(Double, Double). Added Math.Round(Double, Int32, Int32). Added Math.Truncate(Double, Int32, Int32). Modified the list of possible return values to allow for 'Int64.MinValue', 'Int64.MaxValue', 'Double.MinValue', and 'Double.MaxValue' to be returned instead of the standard 'int.MinValue', 'int.MaxValue', 'double.MinValue', and 'double.MaxValue' respectively. Added Math.Round(Single). Added Math.Truncate(Single, Int32, Int32). 1.1.0: The names of the return values has been modified to reflect the fact that some of the Math classes are not intended to represent a specific value. Rather, the Math classes are intended to be used in a functional manner to perform operations on Int64, Double, Single, etc. Return types: Double.MaxValue Double.MinValue Double.NaN Double.PositiveInfinity Double.NegativeInfinity Double.NaN = -Double.MaxValue Double.PositiveInfinity = Double.MaxValue Double.NegativeInfinity = -Double.MaxValue Single.MaxValue Single.MinValue Single.PositiveInfinity



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This article was written by Andy Witte and Jean-Paul Bouchard. Updated October 2010 Table of Contents Overview Millions of integers are used every day to represent the values of financial instruments, the keys of HMRC databases, the products of mechanical drives, the sequences of IP addresses, etc. These integers are usually too large to be represented in the memory of a single computer or machine. The following table summarizes the types of operations that can be performed on an integer represented as a string. The string's characters are, by default, read from right to left. It is also possible to reverse the order of the string before computing any operation. At the same time, Milliseconds (ms) are also represented by strings, and it is also possible to manipulate them by reversing their order or, equivalently, by computing their absolute value. This is usually needed to compare time intervals. Therefore, integers and milliseconds are written as strings but can also be treated like numbers. Moreover, a string is a sequence of characters, so it is also possible to manipulate it as a sequence of characters. In this case, it is not only possible to add two strings (subtract, concatenate etc.) but also to perform shift or transposition operations. To sum up, the set of operations that are compatible with a string are the following: Addition and subtraction Multiplication Integer division Modulus Exponentiation Square root Natural logarithm Logarithm base 2 Logarithm base 10 Comparison Shift/transposition Pow We will now explain the data structures used by this library. Core functions The core functions of MilliMath have been written with performance in mind, especially when dealing with large numbers. The first requirement was to achieve a very high arithmetic throughput, which is the rate at which arithmetic operations are executed. Once a mathematical function has been implemented, the library provides a large number of other functions, such as arithmetics with negative numbers, modular functions, or bitwise operations. The library was designed to be the least space-consuming in memory. Each function only takes a few bytes. This means that the main storage space occupied by the library is the string being operated on. This enables arithmetic functions on large numbers to be performed on these numbers in one step. However, the space saved on the string is not wasted. The library can be used to apply mathematical functions to strings of bytes, to compute their absolute value, or to work on milliseconds represented by strings. Number of bytes It is possible to specify the size of the integers being used by the library in bytes. A byte is the minimum unit of information in the memory of a computer or machine,



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