R's isoreg function generating more knots than unique fitted values

I have been working with R's isoreg function and have experienced a problem: the function is generating more knots than unique fitted values.

From the R help,

iKnots [is an] integer vector giving indices where the fitted curve jumps, i.e., where the convex minorant has kinks

I believe I have an idea about the cause of the problem, and I have a reproducible example:

# Demonstrating the problem
set.seed(100)
x<-runif(88000,0,1)
x<-x[order(x)]
y<- c(rep(c(0.1000001,0.1000000),11000),rep(c(0.1000002,0.1000003),11000),rep(c(0.2000002,0.2000003),11000),rep(1,22000))
plot(test<-isoreg(x,y))
length(unique(test$yf))
length(test$iKnots)

# Evidence of a floating point arithmetic problem
unique(test$yf)
print(c(unique(test$yf)[1],unique(test$yf)[2]),digits=18)
unique(test$yf)[1]==unique(test$yf)[2]
print(c(unique(test$yf)[4],unique(test$yf)[5]),digits=18)
unique(test$yf)[4]==unique(test$yf)[5]}


Here is the plot produced by this example:

You can see that R's isoreg function is identifying many more knots than it should (where there are a lot of red Xs in the plot). However at other places, it correctly uses only 2 knots (the black lines).

It is clear that the problem is connected to R's floating point arithmetic. I also note that isoreg uses .Call to call a C routine to actually do the isotonic regression, so perhaps the problem lies with differences between the C and R languages.

.Call

I am using isoreg to calibrate model probabilities, and I would like to be as precise as possible. Therefore, I have 2 questions:

1) Is there some way I could alter the x and y variables used in the isoreg function to avoid this problem while maintaining as high precision as possible?

2) I can manually find the unique fitted values and the respective knots. However, is this ok? Can I assume that the algorithm found the best fit or could this problem invalidate that assumption?

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