\Header{is.finite}{Finite, Infinite and NaN Numbers}
\alias{is.infinite}{is.finite}
\alias{Inf}{is.finite}
\alias{NaN}{is.finite}
\alias{is.nan}{is.finite}
\keyword{programming}{is.finite}
\keyword{math}{is.finite}
\begin{Usage}
\begin{verbatim}
is.finite(x)
is.infinite(x)
Inf
NaN
is.nan(x)
\end{verbatim}
\end{Usage}
\begin{Description}
\texttt{is.finite} returns a vector of the same length as \texttt{x}
the jth element of which is \texttt{TRUE} if the jth element of \texttt{x} is
finite (i.e. it is not one of the values \texttt{NA}, \texttt{NaN},
\texttt{Inf} or \texttt{-Inf}).

\texttt{is.infinite} returns a vector of the same length as \texttt{x}
the jth element of which is \texttt{TRUE} if the jth element of \texttt{x} is
infinite (i.e. equal to one of \texttt{Inf} or \texttt{-Inf}).\end{Description}
\begin{Examples}
\begin{ExampleCode}
pi / 0 ## = Inf a non-zero number divided by zero creates infinity
0 / 0  ## =  NaN

1/0 + 1/0# Inf
1/0 - 1/0# NaN

1/0 == Inf
1/Inf == 0
exp(-Inf) == 0
## 		(actually, the last one seems to give NA on not-very-new
## 		 versions of Linux, which is a Linux bug and seems to be
## 		 corrected in newer 'libc6' based Linuxen).

is.na(0/0) # T
!is.na(Inf)# T
is.nan(0/0)# T

(!is.nan(NA))  &&  (!is.infinite(NA))  && (!is.finite(NA)) # TRUE!!
( is.nan(NaN)) &&  (!is.infinite(NaN)) && (!is.finite(NaN))# TRUE!!

!is.nan(NA)
all(!is.nan(c(1,NA)))
all(c(F,T,F) == is.nan(c   (1,NaN,NA)))
all(c(F,T,F) == is.nan(list(1,NaN,NA)))#-> FALSE  'BUGlet' [coerce.c]
				# However, S is different anyway.

pi / 0 ## = Inf a non-zero number divided by zero creates infinity
0 / 0  ## =  NaN

1/0 + 1/0# Inf
1/0 - 1/0# NaN

1/0 == Inf
1/Inf == 0
exp(-Inf) == 0
## 		(actually, the last one seems to give NA on not-very-new
## 		 versions of Linux, which is a Linux bug and seems to be
## 		 corrected in newer 'libc6' based Linuxen).

is.na(0/0) # T
!is.na(Inf)# T
is.nan(0/0)# T

(!is.nan(NA))  &&  (!is.infinite(NA))  && (!is.finite(NA)) # TRUE!!
( is.nan(NaN)) &&  (!is.infinite(NaN)) && (!is.finite(NaN))# TRUE!!

!is.nan(NA)
all(!is.nan(c(1,NA)))
all(c(F,T,F) == is.nan(c   (1,NaN,NA)))
all(c(F,T,F) == is.nan(list(1,NaN,NA)))#-> FALSE  'BUGlet' [coerce.c]
				# However, S is different anyway.

lgamma(Inf) == Inf
Inf + Inf == Inf
Inf - Inf == NaN # NA --- should test with  'is.nan()

(1/0) * (1/0)# Inf
(1/0) / (1/0)# NaN

pm <- c(-1,1) # 'pm' = plus/minus

log(0) == - 1/0
exp(-Inf) == 0

sin(Inf)
cos(Inf)
tan(Inf)
all(atan(Inf*pm) == pm*pi/2) # TRUE

x <- c(100,-1e-13,Inf,-Inf, NaN, pi, NA)
x #  1.000000 -3.000000       Inf      -Inf        NA  3.141593        NA
names(x) <- formatC(x, dig=3)
is.finite(x)
##-   100 -1e-13 Inf -Inf NaN 3.14 NA
##-     T      T   .    .   .    T  .
is.na(x)
##-   100 -1e-13 Inf -Inf NaN 3.14 NA
##-     .      .   .    .   T    .  T
which(is.na(x) & !is.nan(x))# only 'NA': 7

is.na(x) | is.finite(x)
##-   100 -1e-13 Inf -Inf NaN 3.14 NA
##-     T      T   .    .   T    T  T
is.infinite(x)
##-   100 -1e-13 Inf -Inf NaN 3.14 NA
##-     .      .   T    T   .    .  .

##-- either  finite or infinite  or  NA:
all(is.na(x) != is.finite(x) | is.infinite(x)) # TRUE
all(is.nan(x) != is.finite(x) | is.infinite(x)) # FALSE: have 'real' NA

##--- Integer
(ix <- structure(as.integer(x),names= names(x)))
##-   100 -1e-13        Inf        -Inf NaN 3.14 NA
##-   100      . 2147483647 -2147483648  NA    3 NA
all(is.na(ix) != is.finite(ix) | is.infinite(ix)) # TRUE (still)

ix[3] == (iI <- as.integer(Inf))#> warning: inaccurate integer conversion!
ix[4] == (imI<- as.integer(-Inf))
iI  == .Machine$integer.max # TRUE
imI == -.Machine$integer.max # TRUE

##--- Overflow in simple integer arithmetic:
as.integer(2)*iI #  -2
as.integer(3)*iI #  2147483645
as.integer(3)*iI == iI-2 # TRUE

storage.mode(ii <- -3:5)
storage.mode(zm <- outer(ii,ii, FUN="*"))# integer
storage.mode(zd <- outer(ii,ii, FUN="/"))# double
range(zd, na.rm=T)# -Inf  Inf
zd[,ii==0]

(storage.mode(print(1:1 / 0:0)))# Inf "double"
(storage.mode(print(1:1 / 1:1)))# 1 "double"
(storage.mode(print(1:1 + 1:1)))# 2 "integer"
(storage.mode(print(2:2 * 2:2)))# 4 "integer"

lgamma(Inf) == Inf
Inf + Inf == Inf
Inf - Inf == NaN # NA --- should test with  'is.nan()

(1/0) * (1/0)# Inf
(1/0) / (1/0)# NaN

pm <- c(-1,1) # 'pm' = plus/minus

log(0) == - 1/0
exp(-Inf) == 0

sin(Inf)
cos(Inf)
tan(Inf)
all(atan(Inf*pm) == pm*pi/2) # TRUE

x <- c(100,-1e-13,Inf,-Inf, NaN, pi, NA)
x #  1.000000 -3.000000       Inf      -Inf        NA  3.141593        NA
names(x) <- formatC(x, dig=3)
is.finite(x)
##-   100 -1e-13 Inf -Inf NaN 3.14 NA
##-     T      T   .    .   .    T  .
is.na(x)
##-   100 -1e-13 Inf -Inf NaN 3.14 NA
##-     .      .   .    .   T    .  T
which(is.na(x) & !is.nan(x))# only 'NA': 7

is.na(x) | is.finite(x)
##-   100 -1e-13 Inf -Inf NaN 3.14 NA
##-     T      T   .    .   T    T  T
is.infinite(x)
##-   100 -1e-13 Inf -Inf NaN 3.14 NA
##-     .      .   T    T   .    .  .

##-- either  finite or infinite  or  NA:
all(is.na(x) != is.finite(x) | is.infinite(x)) # TRUE
all(is.nan(x) != is.finite(x) | is.infinite(x)) # FALSE: have 'real' NA

##--- Integer
(ix <- structure(as.integer(x),names= names(x)))
##-   100 -1e-13        Inf        -Inf NaN 3.14 NA
##-   100      . 2147483647 -2147483648  NA    3 NA
all(is.na(ix) != is.finite(ix) | is.infinite(ix)) # TRUE (still)

ix[3] == (iI <- as.integer(Inf))#> warning: inaccurate integer conversion!
ix[4] == (imI<- as.integer(-Inf))
iI  == .Machine$integer.max # TRUE
imI == -.Machine$integer.max # TRUE

##--- Overflow in simple integer arithmetic:
as.integer(2)*iI #  -2
as.integer(3)*iI #  2147483645
as.integer(3)*iI == iI-2 # TRUE

storage.mode(ii <- -3:5)
storage.mode(zm <- outer(ii,ii, FUN="*"))# integer
storage.mode(zd <- outer(ii,ii, FUN="/"))# double
range(zd, na.rm=T)# -Inf  Inf
zd[,ii==0]

(storage.mode(print(1:1 / 0:0)))# Inf "double"
(storage.mode(print(1:1 / 1:1)))# 1 "double"
(storage.mode(print(1:1 + 1:1)))# 2 "integer"
(storage.mode(print(2:2 * 2:2)))# 4 "integer"
\end{ExampleCode}
\end{Examples}

