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Pairwise summation for dx & dy: minor improvement in computational accuracy #7364

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Pairwise summation for dx & dy: minor improvement in computational accuracy #7364

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12 changes: 8 additions & 4 deletions raster/r.slope.aspect/main.c
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Original file line number Diff line number Diff line change
Expand Up @@ -12,6 +12,7 @@
* Jan-Oliver Wagner <jan intevation.de>,
* Radim Blazek <radim.blazek gmail.com>
* Aaron Saw Min Sern (OpenMP parallelization)
* Akos Halmai (pairwise summation for dx & dy)
* PURPOSE: generates raster maps of slope, aspect, curvatures and
* first and second order partial derivatives from a raster map
* of true elevation values
Expand Down Expand Up @@ -594,6 +595,7 @@ int main(int argc, char *argv[])
double pcurv, tcurv;
double aspect, dnorm1, dx2, dy2, grad2, grad, dxy2;
double key;
double key_sqrt;
double slp_in_perc, slp_in_deg;
int low, hi, test = 0;
bool initialized = false;
Expand Down Expand Up @@ -808,13 +810,15 @@ int main(int argc, char *argv[])
c9 = c5;
}

dx = ((c1 + c4 + c4 + c7) - (c3 + c6 + c6 + c9)) / H;
dy = ((c7 + c8 + c8 + c9) - (c1 + c2 + c2 + c3)) / V;
/* Pairwise summation reduces cancellation errors, this form handles edge cases more reliably. */
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@github-actions github-actions Bot May 2, 2026

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[pre-commit] reported by reviewdog 🐶

Suggested change
/* Pairwise summation reduces cancellation errors, this form handles edge cases more reliably. */
/* Pairwise summation reduces cancellation errors, this form
* handles edge cases more reliably. */

dx = ((c1 + c7) + (c4 + c4) - ((c3 + c9) + (c6 + c6))) / H;
dy = ((c7 + c9) + (c8 + c8) - ((c1 + c3) + (c2 + c2))) / V;
Comment on lines +814 to +815
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@metzm metzm May 3, 2026

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Replace the difference of sums with the sum of differences.


/* compute topographic parameters */
key = dx * dx + dy * dy;
slp_in_perc = 100 * sqrt(key);
slp_in_deg = atan(sqrt(key)) * radians_to_degrees;
key_sqrt = sqrt(key);
slp_in_perc = 100.0 * key_sqrt;
slp_in_deg = radians_to_degrees * atan(key_sqrt);

/* now update min and max */
if (deg) {
Expand Down
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