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`gawk`

`gawk`

uses the GNU MPFR library
for arbitrary precision floating-point arithmetic. The MPFR library
provides precise control over precisions and rounding modes, and gives
correctly rounded, reproducible, platform-independent results. With one
of the command-line options `--bignum` or `-M`,
all floating-point arithmetic operators and numeric functions can yield
results to any desired precision level supported by MPFR.
Two built-in variables, `PREC`

and `ROUNDMODE`

,
provide control over the working precision and the rounding mode
(see Setting Precision, and
see Setting Rounding Mode).
The precision and the rounding mode are set globally for every operation
to follow.

The default working precision for arbitrary precision floating-point values is
53 bits, and the default value for `ROUNDMODE`

is `"N"`

,
which selects the IEEE-754 `roundTiesToEven`

rounding mode
(see Rounding Mode).^{94}
`gawk`

uses the default exponent range in MPFR
(`emax` = 2^30 - 1, `emin` = -`emax`)
for all floating-point contexts.
There is no explicit mechanism to adjust the exponent range.
MPFR does not implement subnormal numbers by default,
and this behavior cannot be changed in `gawk`

.

NOTE:When emulating an IEEE-754 format (see Setting Precision),`gawk`

internally adjusts the exponent range to the value defined for the format and also performs computations needed for gradual underflow (subnormal numbers).

NOTE:MPFR numbers are variable-size entities, consuming only as much space as needed to store the significant digits. Since the performance using MPFR numbers pales in comparison to doing arithmetic using the underlying machine types, you should consider using only as much precision as needed by your program.

• Setting Precision: | Setting the working precision. | |

• Setting Rounding Mode: | Setting the rounding mode. | |

• Floating-point Constants: | Representing floating-point constants. | |

• Changing Precision: | Changing the precision of a number. | |

• Exact Arithmetic: | Exact arithmetic with floating-point numbers. |

The
default precision is 53 bits, since according to the MPFR documentation,
the library should be able to exactly reproduce all computations with
double-precision machine floating-point numbers (`double`

type
in C), except the default exponent range is much wider and subnormal
numbers are not implemented.