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Excel maintains 15 figures in its numbers, but they are not always accurate; mathematically, the bottom line should be the same as the top line, in 'fp-math' the step '1 + 1/9000' leads to a rounding up as the first bit of the 14 bit tail '10111000110010' of the mantissa falling off the table when adding 1 is a '1', this up-rounding is not undone when subtracting the 1 again, since there is no ...
Rather than storing values as a fixed number of bits related to the size of the processor register, these implementations typically use variable-length arrays of digits. Arbitrary precision is used in applications where the speed of arithmetic is not a limiting factor, or where precise results with very large numbers are required.
Elements can be removed from the end of a dynamic array in constant time, as no resizing is required. The number of elements used by the dynamic array contents is its logical size or size, while the size of the underlying array is called the dynamic array's capacity or physical size, which is the maximum possible size without relocating data. [2]
Microsoft Excel is a spreadsheet editor developed by Microsoft for Windows, macOS, Android, iOS and iPadOS.It features calculation or computation capabilities, graphing tools, pivot tables, and a macro programming language called Visual Basic for Applications (VBA).
In Excel and Word 95 and prior editions a weak protection algorithm is used that converts a password to a 16-bit verifier and a 16-byte XOR obfuscation array [1] key. [4] Hacking software is now readily available to find a 16-byte key and decrypt the password-protected document. [5] Office 97, 2000, XP and 2003 use RC4 with 40 bits. [4]
If, for example, the output is constrained to 32-bit integer values, then the hash values can be used to index into an array. Such hashing is commonly used to accelerate data searches. [10] Producing fixed-length output from variable-length input can be accomplished by breaking the input data into chunks of specific size.
In computer programming, a variable-length array (VLA), also called variable-sized or runtime-sized, is an array data structure whose length is determined at runtime, instead of at compile time. [1] In the language C , the VLA is said to have a variably modified data type that depends on a value (see Dependent type ).
For example, 5 is a lower bound for the set S = {5, 8, 42, 34, 13934} (as a subset of the integers or of the real numbers, etc.), and so is 4.On the other hand, 6 is not a lower bound for S since it is not smaller than every element in S.