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In the floating-point case, a variable exponent would represent the power of ten to which the mantissa of the number is multiplied. Languages that support a rational data type usually allow the construction of such a value from two integers, instead of a base-2 floating-point number, due to the loss of exactness the latter would cause.
Programming languages that support arbitrary precision computations, either built-in, or in the standard library of the language: Ada: the upcoming Ada 202x revision adds the Ada.Numerics.Big_Numbers.Big_Integers and Ada.Numerics.Big_Numbers.Big_Reals packages to the standard library, providing arbitrary precision integers and real numbers.
libfixmath is a platform-independent fixed-point math library aimed at developers wanting to perform fast non-integer math on platforms lacking a (or with a low performance) FPU.
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 Go programming language has built-in types complex64 (each component is 32-bit float) and complex128 (each component is 64-bit float). Imaginary number literals can be specified by appending an "i". The Perl core module Math::Complex provides support for complex numbers. Python provides the built-in complex type. Imaginary number literals ...
This alternative definition is significantly more widespread: machine epsilon is the difference between 1 and the next larger floating point number.This definition is used in language constants in Ada, C, C++, Fortran, MATLAB, Mathematica, Octave, Pascal, Python and Rust etc., and defined in textbooks like «Numerical Recipes» by Press et al.
The C99 standard includes new real floating-point types float_t and double_t, defined in <math.h>. They correspond to the types used for the intermediate results of floating-point expressions when FLT_EVAL_METHOD is 0, 1, or 2. These types may be wider than long double. C99 also added complex types: float _Complex, double _Complex, long double ...
Arithmetic underflow can occur when the true result of a floating-point operation is smaller in magnitude (that is, closer to zero) than the smallest value representable as a normal floating-point number in the target datatype. [1] Underflow can in part be regarded as negative overflow of the exponent of the floating-point value. For example ...