How to increase precision to handle very low P-values

Hello, Rlisters

I have to compute p-values that are on the tail of the distribution,
P-values<  10^-20.

However, my current implementations enable one to estimate P-values up to
10^-12, or so.

A typical example is found below, where t is my critical value.

########### example - code adapted from Rassoc #######################

rho01 = 0.5
rho105 = 0.5
rho005  = 0.5
t = 8
z = 2

w0=(rho005-rho01*rho105)/(1-rho01^2)
w1=(rho105-rho01*rho005)/(1-rho01^2)


  fun1=function(t,z){
  return(pnorm((t-rho01*z)/sqrt(1-rho01^2))*dnorm(z))
  }
  fun2=function(t,z){
  return(pnorm(((t-w0*z)/w1-rho01*z)/sqrt(1-rho01^2))*dnorm(z))
  }
  fun3=function(t,z){
  return(pnorm((-t-rho01*z)/sqrt(1-rho01^2))*dnorm(z))
  }

asy=function(t){
z1=2*integrate(function(z){fun1(t,z)},lower=0,upper=t*(1-w1)/w0,subdivisions=1000)$value
z2=2*integrate(function(z){fun2(t,z)},lower=t*(1-w1)/w0,upper=t,subdivisions=1000)$value
z3=-2*integrate(function(z){fun3(t,z)},lower=0,upper=t,subdivisions=500)$value
return(z1+z2+z3)
}

pvalue<-  1-asy(t)
pvalue
  ###########################################

Using this script, my critical values can achieve values up to 7.5, or so.
Above this cutoff my P-values show up as negative values. Why's that?


Grateful for any tips.

All the best,

Alonso


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