Absolute value Totally Explained

Everything about Absolute Value totally explained

In mathematics, the absolute value (or modulus which is Latin for a small measure) of a real number is its numerical value without regard to its sign. So, for example, 3 is the absolute value of both 3 and −3. In computer programming, the mathematical function used to perform this calculation is usually given the name abs.
Generalizations of the absolute value for real numbers occur in a wide variety of mathematical settings. For example an absolute value is also defined for the complex numbers, the quaternions, ordered rings, fields and vector spaces. The absolute value is closely related to the notions of magnitude, distance, and norm in various mathematical and physical contexts.

Real numbers

For any real number a the absolute value or modulus of a is denoted by | a | and is defined as ť

|a| = egin

   The floating-point versions are trickier, as they've to contend with special codes for infinities and not-a-number.
   The function for absolute value in Fortran, Matlab, and GNU Octave is abs. It handles integer, real as well as complex numbers.
   Using assembly language, it's possible to take the absolute value of a register in just three instructions (example shown for a 32-bit register on an x86 architecture, Intel syntax):
cdq xor eax, edx sub eax, edx cdq extends the sign bit of eax into edx. If eax is nonnegative, then edx becomes zero, and the latter two instructions have no effect, leaving eax unchanged. If eax is negative, then edx becomes 0xFFFFFFFF, or -1. The next two instructions then become a two's complement inversion, giving the absolute value of the negative value in eax.

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