round

Function: round
Section: conversions
C-Name: round0
Prototype: GD&
Help: round(x,{&e}): take the nearest integer to all the coefficients of x.
 If e is present, do not take into account loss of integer part precision,
 and set e = error estimate in bits.
Description:
 (small):small:parens   $1
 (int):int:copy:parens  $1
 (real):int             roundr($1)
 (mp):int               mpround($1)
 (mp, &small):int       grndtoi($1, &$2)
 (mp, &int):int         round0($1, &$2)
 (gen):gen              ground($1)
 (gen, &small):gen      grndtoi($1, &$2)
 (gen, &int):gen        round0($1, &$2)
Doc: If $x$ is in $\R$, rounds $x$ to the nearest integer (rounding to
 $+\infty$ in case of ties), then and sets $e$ to the number of error bits,
 that is the binary exponent of the difference between the original and the
 rounded value (the ``fractional part''). If the exponent of $x$ is too large
 compared to its precision (i.e.~$e>0$), the result is undefined and an error
 occurs if $e$ was not given.

 \misctitle{Important remark} Contrary to the other truncation functions,
 this function operates on every coefficient at every level of a PARI object.
 For example
 $$\text{truncate}\left(\dfrac{2.4*X^2-1.7}{X}\right)=2.4*X,$$
 whereas
 $$\text{round}\left(\dfrac{2.4*X^2-1.7}{X}\right)=\dfrac{2*X^2-2}{X}.$$
 An important use of \kbd{round} is to get exact results after an approximate
 computation, when theory tells you that the coefficients must be integers.

Variant: Also available are \fun{GEN}{grndtoi}{GEN x, long *e} and
 \fun{GEN}{ground}{GEN x}.