Create series on invoice totals by month

monthly_range.sql

-- Collect min and max date range
WITH range_values AS (
    SELECT date_trunc('month', min(dat))  as minval,
           date_trunc('month', max(dat))  as maxval
 from IV),

-- Generate date range in monthly intervals
 months as (
    SELECT generate_series(minval, maxval, '1 month'::interval) as month
    from range_values
 )
-- How to join against IV when all I have is a month?
 select mr.month, sum(tot) from months mr
    join iv on mr.month=iv.dat
    where dat between (mr.month - interval '1 month') and mr.month
    group by 1;

         
==== Outputs this (which is wrong ) ====         
         month          |    sum
------------------------+-----------
 1987-05-01 00:00:00+00 |      0.00
 1987-07-01 00:00:00+00 |      0.00
 1987-10-01 00:00:00+00 |   2542.50
 1988-03-01 00:00:00+00 |    487.40
 1988-06-01 00:00:00+00 |    100.00
 1989-02-01 00:00:00+00 |    -60.00
 1990-03-01 00:00:00+00 |     60.00
 1990-05-01 00:00:00+00 |    120.00
 1990-06-01 00:00:00+00 |    105.00
 1990-08-01 00:00:00+00 |    123.50
 1990-10-01 00:00:00+00 |    328.00
 1990-11-01 00:00:00+00 |    147.70
 1991-02-01 00:00:00+00 |    181.34
 1991-03-01 00:00:00+00 |    220.45