IIIF w, size calculation

gistfile1.txt

simeon@RottenApple image_api_size_calc>more 2014-07-25_image_width.py
#!/usr/bin/env python

# In OSD Jon uses: 
#  width_to_request = int(float(desired_height) / image_height * image_width)
# see https://github.com/IIIF/iiif.io/issues/301

matches = 0
for iw in (1,80,200,1234,5678,10567,678991):
    for ih in (1,80,200,1234,5678,10567,678991):
        for dh in (1,2,3,4,80,99,200,217,1234,2679,5678):
            wrf = int(float(dh)/float(ih) * float(iw))
            wri = (dh*iw) / ih 
            if (wrf!=wri):
                print "(%d,%d) -> %d height has %d (by float) != %d (by int) width" %\
                    (iw,ih,dh,wrf,wri)
            else:
                matches+=1
print "%d matching tests not shown" % (matches)

simeon@RottenApple image_api_size_calc>python 2014-07-25_image_width.py
(200,80) -> 5678 height has 14194 (by float) != 14195 (by int) width
(5678,5678) -> 3 height has 2 (by float) != 3 (by int) width
(678991,678991) -> 99 height has 98 (by float) != 99 (by int) width
536 matching tests not shown

If we consider these three non-matching cases:

#1 - python rounding error:

simeon@RottenApple image_api_size_calc>python
Python 2.7.1 (r271:86832, Jul 31 2011, 19:30:53) 
[GCC 4.2.1 (Based on Apple Inc. build 5658) (LLVM build 2335.15.00)] on darwin
Type "help", "copyright", "credits" or "license" for more information.
>>> 5678.0 / 80.0 
70.975
>>> 70.975 * 200
14194.999999999998
>>> int(14194.999999999998)
14194

simeon@RottenApple image_api_size_calc>dc
40k
5678 80 / 200 * p
14195.0000000000000000000000000000000000000000

#2 & #3 - obviously float is at fault because the square start 
image should give a square result