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Representing real numbers using logarithms in R
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########### | |
# S4 class to represent real numbers as logarithms | |
# Includes standard arithmetic operations +,-,*,/, and ^ | |
# Richard D. Morey (richarddmorey@gmail.com) | |
# November 2014 | |
########### | |
# Compute log(exp(a) + exp(b)) | |
logExpAplusExpB <- function(a, b) | |
{ | |
a + log1plusExpA( b - a ) | |
} | |
# Compute log(1 + exp(a)) | |
# From plogis.c | |
log1plusExpA <- function(a) | |
{ | |
if( a <= 18 ) return( log1p( exp(a) ) ) | |
if( a > 33.3 ) return( a ) | |
# else: 18.0 < x <= 33.3 : | |
return( a + exp( -a ) ) | |
} | |
# Compute log(exp(a) - exp(b)) | |
logExpAminusExpB <- function(a, b) | |
{ | |
a + pexp( a - b, log.p=TRUE ) | |
} | |
setClass("logRepresentedReal", | |
representation(modulo = "numeric" , | |
sign ="integer") | |
) | |
logRepresentedReal <- function( modulo, sign ){ | |
new( "logRepresentedReal", modulo = modulo, sign = sign ) | |
} | |
setValidity("logRepresentedReal", function(object){ | |
if( abs(object@sign) != 1 ) return("Sign must be 1 or -1.") | |
return(TRUE) | |
}) | |
setMethod("show", signature("logRepresentedReal"), function(object){ | |
# Use the function in the BayesFactor package to print | |
# logarithmically-represented values nicely | |
require(BayesFactor, quietly = TRUE) | |
str = BayesFactor:::expString(object@modulo) | |
sgn = "" | |
if(object@sign < 0) sgn = "-" | |
cat(paste(" ", sgn, str, " ", sep="")) | |
}) | |
setAs("logRepresentedReal", "numeric", function( from, to ){ | |
as.double.logRepresentedReal(from) | |
}) | |
as.double.logRepresentedReal <- function(x){ | |
x@sign * exp(x@modulo) | |
} | |
setMethod("abs", signature("logRepresentedReal"), function(x){ | |
x@sign = 1L | |
return(x) | |
}) | |
setMethod("sign", signature("logRepresentedReal"), function(x){ | |
x@sign | |
}) | |
setMethod("-", signature("logRepresentedReal"), function(e1){ | |
e1@sign = as.integer(-e1@sign) | |
return(e1) | |
}) | |
setMethod('>', signature("logRepresentedReal", "logRepresentedReal"), function(e1, e2){ | |
if( (e1@modulo == e2@modulo) & (e1@sign == e2@sign) ) return(FALSE) | |
if(sign(e1) > sign(e2)) return(TRUE) | |
if(sign(e1) < sign(e2)) return(FALSE) | |
if(sign(e1) == 1) return(e1@modulo > e2@modulo) | |
if(sign(e1) == -1) return(e1@modulo < e2@modulo) | |
}) | |
setMethod('<', signature("logRepresentedReal", "logRepresentedReal"), function(e1, e2){ | |
if( (e1@modulo == e2@modulo) & (e1@sign == e2@sign) ) return(FALSE) | |
return(!(e1>e2)) | |
}) | |
setGeneric("is.zero", function(x){ | |
standardGeneric("is.zero") | |
}) | |
setMethod("is.zero", signature("logRepresentedReal"), function(x){ | |
if( !is.infinite(x@modulo) ) return(FALSE) | |
if(sign(x) != sign(x@modulo)) return(TRUE) | |
return(FALSE) | |
}) | |
setMethod("is.infinite", signature("logRepresentedReal"), function(x){ | |
if( !is.infinite(x@modulo) ) return(FALSE) | |
if(sign(x) == sign(x@modulo)) return(TRUE) | |
return(FALSE) | |
}) | |
setMethod("is.finite", signature("logRepresentedReal"), function(x){ | |
return(!is.infinite(x)) | |
}) | |
setMethod('+', signature("logRepresentedReal", "logRepresentedReal"), function(e1, e2){ | |
if(e1@sign == 1 & e2@sign == -1 ) return(e1 - -e2) | |
if(e1@sign == -1 & e2@sign == -1 ) return( -(-e1 + -e2) ) | |
if(e1@sign == -1 & e2@sign == 1 ) return(e2 - -e1) | |
logsum = logExpAplusExpB(e1@modulo, e2@modulo) | |
logRepresentedReal( logsum, 1L ) | |
}) | |
setMethod('+', signature("logRepresentedReal", "numeric"), function(e1, e2){ | |
if( e2 == 0 ) return(e1) | |
e2 = logRepresentedReal( log(abs(e2)), as.integer(sign(e2)) ) | |
e1 + e2 | |
}) | |
setMethod('+', signature("numeric","logRepresentedReal"), function(e1, e2){ | |
e2 + e1 | |
}) | |
setMethod('-', signature("logRepresentedReal", "logRepresentedReal"), function(e1, e2){ | |
if(e1@sign == 1 & e2@sign == -1 ) return( e1 + -e2 ) | |
if(e1@sign == -1 & e2@sign == -1 ) return( -abs(e1) + abs(e2) ) | |
if(e1@sign == -1 & e2@sign == 1 ) return( -(e2 + -e1) ) | |
if(e1 > e2){ | |
logdiff = logExpAminusExpB(e1@modulo, e2@modulo) | |
return(logRepresentedReal( logdiff, 1L )) | |
}else if(e1 < e2){ | |
logdiff = logExpAminusExpB(e2@modulo, e1@modulo) | |
return(logRepresentedReal( logdiff, -1L )) | |
}else{ | |
return(logRepresentedReal( -Inf, 1L )) | |
} | |
}) | |
setMethod('-', signature("logRepresentedReal", "numeric"), function(e1, e2){ | |
if( e2 == 0 ) return(e1) | |
e2 = logRepresentedReal( log(abs(e2)), as.integer(sign(e2)) ) | |
e1 - e2 | |
}) | |
setMethod('-', signature("numeric","logRepresentedReal"), function(e1, e2){ | |
-e2 + e1 | |
}) | |
setMethod('*', signature("numeric", "logRepresentedReal"), function(e1, e2){ | |
sgn = sign(e1) * sign(e2) | |
modu = log(abs(e1)) + e2@modulo | |
logRepresentedReal( modu, as.integer(sgn) ) | |
}) | |
setMethod('*', signature("logRepresentedReal", "numeric"), function(e1, e2){ | |
e2 * e1 | |
}) | |
setMethod('*', signature("logRepresentedReal", "logRepresentedReal"), function(e1, e2){ | |
sgn = sign(e1) * sign(e2) | |
modu = e1@modulo + e2@modulo | |
logRepresentedReal( modu, as.integer(sgn) ) | |
}) | |
setMethod('/', signature("logRepresentedReal", "logRepresentedReal"), function(e1, e2){ | |
sgn = sign(e1) * sign(e2) | |
modu = e1@modulo - e2@modulo | |
logRepresentedReal( modu, as.integer(sgn) ) | |
}) | |
setMethod('/', signature("numeric", "logRepresentedReal"), function(e1, e2){ | |
if(e1 == 1){ | |
e2@modulo = -e2@modulo | |
return(e2) | |
}else{ | |
return(e1 * (1/e2)) | |
} | |
}) | |
setMethod('/', signature("logRepresentedReal", "numeric"), function(e1, e2){ | |
1/(e2/e1) | |
}) | |
setMethod('^', signature("logRepresentedReal", "numeric"), function(e1, e2){ | |
if( e2 == 0 ) | |
return( logRepresentedReal( 0, 1L ) ) | |
if( sign(e1)==1 | e2%%2 == 0 ){ | |
sgn = 1L | |
}else{ | |
sgn = -1L | |
} | |
if(e2 < 0){ | |
e2 = abs(e2) | |
e1 = 1/e1 | |
} | |
modu = e1@modulo * e2 | |
logRepresentedReal( modu, as.integer(sgn) ) | |
}) | |
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