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The IBM 1130, sold in 1965, [2] offered two floating-point formats: A 32-bit "standard precision" format and a 40-bit "extended precision" format. Standard-precision format contains a 24-bit two's complement significand while extended-precision utilizes a 32-bit two's complement significand. The latter format makes full use of the CPU's 32-bit ...
Arbitrary-precision arithmetic can also be used to avoid overflow, which is an inherent limitation of fixed-precision arithmetic. Similar to an automobile's odometer display which may change from 99999 to 00000, a fixed-precision integer may exhibit wraparound if numbers grow too large to represent at the fixed level of precision.
In POSIX-compliant operating systems, the header math.h shall declare and the mathematical library libm shall provide the functions erf and erfc (double precision) as well as their single precision and extended precision counterparts erff, erfl and erfcf, erfcl.
Double-precision floating-point format (sometimes called FP64 or float64) is a floating-point number format, usually occupying 64 bits in computer memory; it represents a wide range of numeric values by using a floating radix point. Double precision may be chosen when the range or precision of single precision would be insufficient.
An extended precision format extends a basic format by using more precision and more exponent range. An extendable precision format allows the user to specify the precision and exponent range. An implementation may use whatever internal representation it chooses for such formats; all that needs to be defined are its parameters ( b , p , and emax ).
It is related to precision in mathematics, which describes the number of digits that are used to express a value. Some of the standardized precision formats are: Half-precision floating-point format; Single-precision floating-point format; Double-precision floating-point format; Quadruple-precision floating-point format
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.
With gcc on Linux, 80-bit extended precision is the default; on several BSD operating systems (FreeBSD and OpenBSD), double-precision mode is the default, and long double operations are effectively reduced to double precision. [22] (NetBSD 7.0 and later, however, defaults to 80-bit extended precision [23]).