PostgreSQL pnorm() function calculated the c.d.f. of the normal Gaussian distribution. This function match's R's build in pnorm() function to within +/- 2e-7 over the entire real line. However, it's a constant 1/0 above/below z=+7/-7.

pnorm.sql

CREATE OR REPLACE FUNCTION pnorm(z double precision) RETURNS double precision AS $$
  SELECT CASE 
  	WHEN $1 >= 0 THEN 1 - POWER(((((((0.000005383*$1+0.0000488906)*$1+0.0000380036)*$1+0.0032776263)*$1+0.0211410061)*$1+0.049867347)*$1+1),-16)/2
  	ELSE 1 - pnorm(-$1)
  END;
$$ LANGUAGE SQL IMMUTABLE STRICT;

Thank you very much for the function! Really helps converting z-scores for the CDC growth charts.