+// The weight function can be expensive to compute over and over again
+// (which will happen during e.g. a zoom), but it is also easy to interpolate
+// linearly. We compute the right half of the function (in the range of
+// 0..LANCZOS_RADIUS), with two guard elements for easier interpolation, and
+// linearly interpolate to get our function.
+//
+// We want to scale the table so that the maximum error is always smaller
+// than 1e-6. As per http://www-solar.mcs.st-andrews.ac.uk/~clare/Lectures/num-analysis/Numan_chap3.pdf,
+// the error for interpolating a function linearly between points [a,b] is
+//
+// e = 1/2 (x-a)(x-b) f''(u_x)
+//
+// for some point u_x in [a,b] (where f(x) is our Lanczos function; we're
+// assuming LANCZOS_RADIUS=3 from here on). Obviously this is bounded by
+// f''(x) over the entire range. Numeric optimization shows the maximum of
+// |f''(x)| to be in x=1.09369819474562880, with the value 2.40067758733152381.
+// So if the steps between consecutive values are called d, we get
+//
+// |e| <= 1/2 (d/2)^2 2.4007
+// |e| <= 0.1367 d^2
+//
+// Solve for e = 1e-6 yields a step size of 0.0027, which to cover the range
+// 0..3 needs 1109 steps. We round up to the next power of two, just to be sure.
+//
+// You need to call lanczos_table_init_done before the first call to
+// lanczos_weight_cached.
+#define LANCZOS_TABLE_SIZE 2048
+bool lanczos_table_init_done = false;
+float lanczos_table[LANCZOS_TABLE_SIZE + 2];
+
+void init_lanczos_table()
+{
+ for (unsigned i = 0; i < LANCZOS_TABLE_SIZE + 2; ++i) {
+ lanczos_table[i] = lanczos_weight(float(i) * (LANCZOS_RADIUS / LANCZOS_TABLE_SIZE));
+ }
+ lanczos_table_init_done = true;
+}
+
+float lanczos_weight_cached(float x)
+{
+ x = fabs(x);
+ if (x > LANCZOS_RADIUS) {
+ return 0.0f;
+ }
+ float table_pos = x * (LANCZOS_TABLE_SIZE / LANCZOS_RADIUS);
+ int table_pos_int = int(table_pos); // Truncate towards zero.
+ float table_pos_frac = table_pos - table_pos_int;
+ assert(table_pos < LANCZOS_TABLE_SIZE + 2);
+ return lanczos_table[table_pos_int] +
+ table_pos_frac * (lanczos_table[table_pos_int + 1] - lanczos_table[table_pos_int]);
+}
+