Precision issues for high resolution images

[astrofrog]

I'm running into precision issues for images that are in the 0.01" resolution regime (ALMA, JWST, etc.). Here is a minimal example to reproduce. First, generate test images with the following Python code:

import numpy as np
from astropy.wcs import WCS
from astropy.io import fits

for label, res in [('high', 3e-6), ('low', 1e-3)]:

    wcs1 = WCS()
    wcs1.wcs.ctype = 'RA---TAN', 'DEC--TAN'
    wcs1.wcs.crval = 13, 20
    wcs1.wcs.crpix = 10.1, 10.2
    wcs1.wcs.cdelt = res, res

    wcs2 = WCS()
    wcs2.wcs.ctype = 'RA---TAN', 'DEC--TAN'
    wcs2.wcs.crval = 13, 20
    wcs2.wcs.crpix = 3, 3
    wcs2.wcs.cdelt = 3 * res, 3 * res

    array = np.zeros((19, 19))
    array[9, 9] = 1

    fits.writeto(f'data1_{label}.fits', array, wcs1.to_header(), overwrite=True)
    fits.writeto(f'data2_{label}.fits', array, wcs2.to_header(), overwrite=True)

then run Montage with e.g.:

#!/bin/bash

Montage/bin/mGetHdr data2_high.fits header2_high.hdr
Montage/bin/mProject data1_high.fits data3_high.fits header2_high.hdr

Montage/bin/mGetHdr data2_low.fits header2_low.hdr
Montage/bin/mProject data1_low.fits data3_low.fits header2_low.hdr

(I could also have used the Python API but just doing it the simplest way to minimize any potential issues)

Finally, check the results in Python - as the resolution has changed by a factor of 3, the total flux in the image should be changed by a factor of 9, so the following should return 1:

from astropy.io import fits

result_high = fits.getdata('data3_high.fits')
result_low = fits.getdata('data3_low.fits')

print(result_high.sum() * 9)
print(result_low.sum() * 9)

However, this gives:

0.84375
0.9999990280958064

The result for the low resolution is as expected, but for the high resolution is significantly wrong (and diverges fast as the resolution is lowered further).

I tried to dig into the C code but I couldn't determine what might be going wrong. All the calculations are done in double precision but there must be some loss of precision in one of the calculations.