Search results
Results from the WOW.Com Content Network
In approximate arithmetic, such as floating-point arithmetic, the distributive property of multiplication (and division) over addition may fail because of the limitations of arithmetic precision. For example, the identity 1 / 3 + 1 / 3 + 1 / 3 = ( 1 + 1 + 1 ) / 3 {\displaystyle 1/3+1/3+1/3=(1+1+1)/3} fails in decimal arithmetic , regardless of ...
A floating-point system can be used to represent, with a fixed number of digits, numbers of very different orders of magnitude — such as the number of meters between galaxies or between protons in an atom. For this reason, floating-point arithmetic is often used to allow very small and very large real numbers that require fast processing times.
By contrast, in computer science, addition and multiplication of floating point numbers are not associative, as different rounding errors may be introduced when dissimilar-sized values are joined in a different order. [7] To illustrate this, consider a floating point representation with a 4-bit significand:
Variable length arithmetic represents numbers as a string of digits of a variable's length limited only by the memory available. Variable-length arithmetic operations are considerably slower than fixed-length format floating-point instructions.
The commutative property can also be easily ... distributive and scalar ... The straightforward algorithm for calculating a floating-point dot product of vectors ...
In computing, the modulo operation returns the remainder or signed remainder of a division, after one number is divided by another, called the modulus of the operation.. Given two positive numbers a and n, a modulo n (often abbreviated as a mod n) is the remainder of the Euclidean division of a by n, where a is the dividend and n is the divisor.
The advantage of decimal floating-point representation over decimal fixed-point and integer representation is that it supports a much wider range of values. For example, while a fixed-point representation that allocates 8 decimal digits and 2 decimal places can represent the numbers 123456.78, 8765.43, 123.00, and so on, a floating-point ...
Archimedean property: for every real number x, there is an integer n such that < (take, = +, where is the least upper bound of the integers less than x). Equivalently, if x is a positive real number, there is a positive integer n such that 0 < 1 n < x {\displaystyle 0<{\frac {1}{n}}<x} .