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# Fixed and Arbitrary Precision Numerical Fields

Sage supports two optimized fixed precision fields for numerical computation, the real double (RealDoubleField) and complex double fields (ComplexDoubleField). Sage also supports arbitrary precision real (RealField) and complex fields (ComplexField), and real and complex interval arithmetic (RealIntervalField and ComplexIntervalField).

Real and complex double elements are optimized implementations that use the GNU Scientific Library for arithmetic and some special functions. Arbitrary precision real and complex numbers are implemented using the MPFR library, which builds on GMP. (Note that Sage doesn’t currently use the MPC library.) The interval arithmetic field is implemented using the MPFI library.

In many cases the PARI C-library is used to compute special functions when implementations aren’t otherwise available.

- Double Precision Real Numbers
- Arbitrary Precision Real Numbers
- Arbitrary Precision Real Intervals
- Field of Arbitrary Precision Real Number Intervals
- File: sage/rings/real_interval_absolute.pyx (starting at line 1)
- These classes are very lazy, in the sense that it doesn’t really do anything
- Double Precision Complex Numbers
- Field of Arbitrary Precision Complex Numbers
- Arbitrary Precision Complex Numbers
- Arbitrary Precision Complex Numbers using GNU MPC
- Field of Arbitrary Precision Complex Intervals
- Arbitrary Precision Complex Intervals

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