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## D.14 `mpfr`

The `mpfr` library provides a rich assortment of floating point operations on arbitrary precision numbers (http://www.mpfr.org). These numbers are represented in a format that is not binary compatible with the standard IEEE floating point number format used by other libraries, but they offer superior numerical stability suitable for many ill conditioned problems.

The virtual code interface to the `mpfr` library follows the native API to the extent of using the same names for most operations, but excludes features pertaining to i/o, mutable storage, and memory management.

The `mpfr` library functions are invoked by an expression of the form

    library('mpfr',f)

Aside from a few exceptions as noted, `f` is a character string derived from the name of the related function from the `mpfr` C library as documented at the above address, but without the `mpfr_` prefix.

The full complement of available functions is documented in the remainder of this section.

- References to natural numbers pertain to the list representation described in Representation of Numeric and Textual Data.
- All functions that perform rounding use a mode of `GMP_RNDN` for rounding to nearest, which is not explicitly specified on the virtual side.

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