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Hats: choose the tiling's starting hat more uniformly.

This fills in the missing piece of commit 6f75879e9fe7cb5, which was
trying to make the output patches of tiling as uniformly random as
possible across the whole space of possible ones. I fixed every
_intermediate_ step in the algorithm, but forgot the starting one!

--- a/hat.c

+++ b/hat.c

@@ -497,6 +497,28 @@

     lenof(parents_H), lenof(parents_T), lenof(parents_P), lenof(parents_F),

 };

+/*

+ * Similarly, we also want to choose our absolute starting hat with

+ * close to uniform probability, which again we do by looking at the

+ * limiting ratio of the metatile types, and this time, scaling by the

+ * number of hats in each metatile.

+ *

+ * We cheatingly use the same MetatilePossibleParent struct, because

+ * it's got all the right fields, even if it has an inappropriate

+ * name.

+ */

+static const MetatilePossibleParent starting_hats[] = {

+    { TT_H,  0, PROB_H },

+    { TT_H,  1, PROB_H },

+    { TT_H,  2, PROB_H },

+    { TT_H,  3, PROB_H },

+    { TT_T,  0, PROB_P },

+    { TT_P,  0, PROB_P },

+    { TT_P,  1, PROB_P },

+    { TT_F,  0, PROB_F },

+    { TT_F,  1, PROB_F },

+};

+

 #undef PROB_H

 #undef PROB_T

 #undef PROB_P

@@ -624,15 +646,17 @@

 static void init_coords_random(HatCoordContext *ctx, random_state *rs)

 {

+    const MetatilePossibleParent *starting_hat = choose_mpp(

+        rs, starting_hats, lenof(starting_hats));

+

     ctx->rs = rs;

     ctx->prototype = hc_new();

     hc_make_space(ctx->prototype, 3);

-    ctx->prototype->c[0].type = TT_KITE;

-    ctx->prototype->c[1].type = TT_HAT;

-    ctx->prototype->c[2].type = random_upto(rs, 4);

+    ctx->prototype->c[2].type = starting_hat->type;

     ctx->prototype->c[2].index = -1;

-    ctx->prototype->c[1].index = random_upto(

-        rs, hats_in_metatile[ctx->prototype->c[2].type]);

+    ctx->prototype->c[1].type = TT_HAT;

+    ctx->prototype->c[1].index = starting_hat->index;

+    ctx->prototype->c[0].type = TT_KITE;

     ctx->prototype->c[0].index = random_upto(rs, HAT_KITES);

     ctx->prototype->nc = 3;

 }