Make Tile swap slow at a low Swap rate, on a curved slider

A tile has to come back to the cut it started with for the clip to
loop, so every tile swapped at least twice a clip, and below that
rounding left every tile still: the bottom of the slider was either
frozen or busy. Swap rate is now the average per tile: below two swaps
a clip only a share of the tiles swap (twice each), fewer the lower it
goes, and above it each tile rounds up or down by its own draw.

ParamSpec::slider() takes an optional curve: the scale runs over the
slider's travel and sliderValue/sliderPosition map it onto the number
as position^curve. Swap rate uses a curve of 3, so the low end gets
most of the slider; the command line and project file are unchanged.

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>

tests/core_tests.cpp

@@ -4,8 +4,10 @@
 #include <array>
 #include <atomic>
 #include <clocale>
+#include <cmath>
 #include <cstdio>
 #include <cstdlib>
+#include <cstring>
 #include <filesystem>
 #include <fstream>
 #include <iostream>
@@ -2079,6 +2081,37 @@ int main() {
             frozenSwap.values["tileswap_rate"] = 0.0;
             check(sameBytes(frameOf(frozenSwap, 0), frameOf(frozenSwap, 5)),
                   "at a rate of 0 it holds still");
+            // How many pixels ever show something other than frame 0.
+            auto moving = [&](const ChainStage& at) {
+                const auto first = frameOf(at, 0);
+                std::vector<bool> moved(static_cast<std::size_t>(80 * 48), false);
+                for (int index = 1; index < 8; ++index) {
+                    const auto frame = frameOf(at, index);
+                    for (int y = 0; y < 48; ++y) {
+                        for (int x = 0; x < 80; ++x) {
+                            if (std::memcmp(frame.row(y) + x * 3, first.row(y) + x * 3, 3) != 0) {
+                                moved[static_cast<std::size_t>(y * 80 + x)] = true;
+                            }
+                        }
+                    }
+                }
+                return std::count(moved.begin(), moved.end(), true);
+            };
+            ChainStage slowSwap = swapStage;
+            slowSwap.values["tileswap_rate"] = 0.3;
+            const auto slowMoving = moving(slowSwap);
+            check(slowMoving > 0 && slowMoving < moving(swapStage),
+                  "a rate below two swaps a clip moves only some of the tiles");
+
+            const auto& rate = swap->params().back();
+            check(rate.onSlider && rate.curve > 1.0, "its swap rate is a curved slider");
+            check(rate.sliderValue(0.0) == 0.0 && rate.sliderValue(1.0) == 5.0 &&
+                      rate.sliderValue(0.5) < 2.5,
+                  "which spans the whole range and gives the low end more travel");
+            check(std::abs(rate.sliderValue(rate.sliderPosition(0.37)) - 0.37) < 1e-9 &&
+                      rate.sliderValue(0.123456) * 100.0 ==
+                          std::round(rate.sliderValue(0.123456) * 100.0),
+                  "a value finds its place on the slider, and a place rounds to the step");
             ChainStage scattered = swapStage;
             scattered.values["tileswap_layout"] = std::string("scatter");
             ChainStage bricks = swapStage;