Floating-Point Algebra

Simply stated, floating-point algebra is algebra performed on floating-point representations by any number of automated devices.

Traditionally, this definition is phrased so as to apply only to algebra performed on floating-point representations of real numbers (i.e., to finite elements of the collection of floating-point numbers) though several additional types of floating-point data including signed infinities and NaNs are also commonly allowed as inputs for such functions. In many widely-adopted standards, e.g., IEEE 754-2008, floating-point algebra falls under the larger heading of floating-point arithmetic.

operation	function	domain	possible exceptions
sin			Invalid Operation (if ); Underflow
cos			Invalid Operation (if ); Underflow
tan			Invalid Operation (if ); Underflow
sinPi			Invalid Operation (if ); Underflow; Several cases
cosPi			Invalid Operation (if ); Several cases
asin			Invalid Operation (if ); Underflow
acos			Invalid Operation (if )
atan			Underflow
atanPi			Underflow
	see below		Underflow; Several cases
	see below		Underflow
sinh			Overflow; Underflow
cosh			Overflow
tanh			Underflow
asinh			Underflow
acosh			Invalid Operation (if )
atanh			Underflow; Divide By Zero (if ); Invalid Operation (if )

The above table summarizes the algebraic functions included in IEEE 754-2008 under the heading "recommended arithmetic operations." Note that trigonometric functions are included as well.

Note that the exact definition of the function is omitted from the table but is the angle subtended at the origin by the point and the positive x-axis having range ; similarly, is a normalized version of the same function having scaled range . Other details and caveats of the functions mentioned throughout can be found in the documentation (IEEE Computer Society 2008, §5 and §9); the exceptions labeled "Several cases" are also addressed in detail (IEEE Computer Society 2008, pp 43-45).