From: Søren Sandmann Pedersen <soren.sandm...@gmail.com> There are a few bugs in the current normalization code
(1) The normalization is based on the sum of the *floating point* values generated by integral(). But in order to get the sum to be close to pixman_fixed_1, the sum of the rounded fixed point values should be used. (2) The multiplications in the normalization loops often round the same way, so the residual error can fairly large. (3) The residual error is added to the sample located at index (width - width / 2), which is not the midpoint for odd widths (and for width 1 is in fact outside the array). This patch fixes these issues by (1) using the sum of the fixed point values as the total to divide by, (2) doing error diffusion in the normalization loop. Changes in this version: Keep the total as a pixman_fixed_t. Merge the .5 offset used for rounding into the e value. This produces the same results but matches how I have seen error diffusion done. The possible error range at the end contains only one integer, zero. Floating point rounding errors will not change this unless there are more than 2^20 samples in the filter. So there is never any possible way to add the residual error, so the code for this is removed. Signed-off-by: Bill Spitzak <spit...@gmail.com> --- pixman/pixman-filter.c | 32 ++++++++++++++++++-------------- 1 file changed, 18 insertions(+), 14 deletions(-) diff --git a/pixman/pixman-filter.c b/pixman/pixman-filter.c index 11e7d0e..b3c36b8 100644 --- a/pixman/pixman-filter.c +++ b/pixman/pixman-filter.c @@ -245,9 +245,9 @@ create_1d_filter (int width, for (i = 0; i < n_phases; ++i) { double frac = step / 2.0 + i * step; - pixman_fixed_t new_total; + pixman_fixed_t total; int x, x1, x2; - double total; + double e; /* Sample convolution of reconstruction and sampling * filter. See rounding.txt regarding the rounding @@ -278,24 +278,28 @@ create_1d_filter (int width, ihigh - ilow); } - total += c; - *p++ = (pixman_fixed_t)(c * 65536.0 + 0.5); - } + *p = (pixman_fixed_t)floor (c * 65536.0 + 0.5); + total += *p; + p++; + } - /* Normalize */ + /* Normalize, with error diffusion */ p -= width; - total = 1 / total; - new_total = 0; + e = 0.5; for (x = x1; x < x2; ++x) { - pixman_fixed_t t = (*p) * total + 0.5; - - new_total += t; + double v = (*p) * 65536.0 / total + e; + pixman_fixed_t t = floor (v); + e = v - t; *p++ = t; } - - if (new_total != pixman_fixed_1) - *(p - width / 2) += (pixman_fixed_1 - new_total); + /* The sum of all the t values calculated above is 65536.5 - e + * (where e is the final value of e). This can be seen because + * total == sum(*p). Since 0 <= e <= 1 the only integer in + * range is 65536. So there can be no remaining error. For a + * few dozen entries in which can vary by no more than 2^16 + * double precision error does not effect this result. + */ } } -- 1.9.1 _______________________________________________ Pixman mailing list Pixman@lists.freedesktop.org https://lists.freedesktop.org/mailman/listinfo/pixman