#! /usr/bin/env python

# Combining multiple (independent) ranges assuming log-normal distributions
# Usage example:
#    combine.py 19..21 28..32
#
# Copyright 2009 Sanjoy Mahajan.  This is free software.
# License: GNU GPLv3 (or any later version, at your option).

from sys import argv, stderr, exit
from math import log, exp, sqrt

def help():
    print '''Usage: 
  %s [/]l1..u1 [/]l2..u2 ...

A range preceded by a / means to divide, rather than multiply, by
that range.  A range with no .. is shorthand for N..N (a range with
ratio 1).

The output is the combined range in the form lower..midpoint..upper

Examples:
  %s 1..2 1..2       => 1.22509..2..3.26505
  %s                 => 1.22509..2..3.26505
  %s 1..2 2..3 /3..4 => 0.652789..1..1.53189''' % ((argv[0],)*4)

if len(argv) == 1 or argv[1] in ['-h', '--help']:
    help()
    exit()

lower = upper = 1
log_width_squared = 0
for qty in argv[1:]:
    divide = False
    if qty[0] == '/':
        divide = True
        qty = qty[1:]
    numbers = [float(s) for s in qty.split('..')]
    if len(numbers) == 3:        # ignore midpoint, if given
        l, u  =  numbers[0], numbers[2]
    elif len(numbers) == 1:     # a sure value
        l, u = numbers[0], numbers[0]
    else:
        l, u  =  numbers
    if divide:
        l, u = 1/u, 1/l
    lower *= l
    upper *= u
    log_width_squared += log(u/l)**2
mean  = sqrt(lower*upper)
ratio = exp(0.5*sqrt(log_width_squared))
print "%g..%g..%g" % (mean/ratio, mean, mean*ratio)