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code.google.com /p /libfixmath 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 .
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.
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 C++ standard library provides a complex template class as well as complex-math functions in the <complex> header. 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".
For example, gcc provides a quadruple-precision type called __float128 for x86, x86-64 and Itanium CPUs, [22] and on PowerPC as IEEE 128-bit floating-point using the -mfloat128-hardware or -mfloat128 options; [23] and some versions of Intel's C/C++ compiler for x86 and x86-64 supply a nonstandard quadruple-precision type called _Quad. [24]
Swift introduced half-precision floating point numbers in Swift 5.3 with the Float16 type. [20] OpenCL also supports half-precision floating point numbers with the half datatype on IEEE 754-2008 half-precision storage format. [21] As of 2024, Rust is currently working on adding a new f16 type for IEEE half-precision 16-bit floats. [22]
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.
In a normal floating-point value, there are no leading zeros in the significand (also commonly called mantissa); rather, leading zeros are removed by adjusting the exponent (for example, the number 0.0123 would be written as 1.23 × 10 −2). Conversely, a denormalized floating-point value has a significand with a leading digit of zero.