Incorrect behaviour of CCDFs when there is a negative random variable

From @randommm on November 20, 2014 1:55

The following program:

transformed data {
  int y[2];
  y[1] <- 0;
  y[2] <- 1;
  print(poisson_ccdf_log(0, 5));
  print(poisson_ccdf_log(1, 5));
  print(poisson_ccdf_log(y, 5));
}
parameters {
  real any;
}
model {
  any ~ normal(0, 1);  
}

Outputs:

-0.00676075
-0.0412676
-0.0480283

(the last number is the sum of the first two as expected)

However, the following program:

transformed data {
  int y[2];
  y[1] <- -1;
  y[2] <- 1;
  print(poisson_ccdf_log(-1, 5));
  print(poisson_ccdf_log(1, 5));
  print(poisson_ccdf_log(y, 5));
}
parameters {
  real any;
}
model {
  any ~ normal(0, 1);  
}

Outputs:

0
-0.0412676
0

Which doesn't make sense: the last number should have been -0.0412676 too.

The way the CCDFs are currently designed makes them ignore everything when there is a negative random variable inside the vector of random variables:

  // Explicit return for extreme values
  // The gradients are technically ill-defined, but treated as neg infinity
  for (size_t i = 0; i < stan::length(n); i++) {
    if (value_of(n_vec[i]) < 0) 
      return operands_and_partials.to_var(0.0);
  }

Copied from original issue: stan-dev/stan#1142