Rewrite on libavr

Same controller: thermistor on ADC0 averaged over 1000 free-running
conversions, 50 kHz fan PWM on OC0B, 115200 Bd console with the full
command set, EEPROM temperature histogram, watchdog-reset path into the
boot section. The Steinhart-Hart math and the libm log are gone — the
Beta equation and the cubic fan curve are consteval-evaluated into
flash tables; the firmware never does floating point. Byte-identical
.text in both libavr modes. Legacy stays on master.

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

src/statistics.hpp

@@ -0,0 +1,105 @@
+#pragma once
+
+#include <array>
+#include <cstdint>
+
+#include <libavr/libavr.hpp>
+
+#include "board.hpp"
+
+// Temperature histogram: one uint32 bucket per °C 0..99, sampled once a
+// second, written back to EEPROM every 30 minutes (update() only touches
+// changed bytes). Erased EEPROM reads back as 0xffffffff — treated as 0.
+namespace app {
+
+class statistics {
+	static constexpr std::uint8_t range = 100;
+	static constexpr std::uint32_t sample_delay_ms = 1'000;
+	static constexpr std::uint32_t writeback_delay_ms = 1'800'000;
+
+	using stored = avr::eeprom::var<std::array<std::uint32_t, range>, 0>;
+
+	static inline std::array<std::uint32_t, range> histogram{};
+	static inline std::uint64_t last_sample = 0;
+	static inline std::uint64_t last_writeback = 0;
+
+	static constexpr std::uint8_t clamp(std::int8_t t)
+	{
+		return t < 0 ? 0 : (t >= range ? range - 1 : static_cast<std::uint8_t>(t));
+	}
+
+  public:
+	static constexpr auto claims = stored::claims;
+
+	static void init()
+	{
+		histogram = stored::read();
+		for (auto &bucket : histogram)
+			if (bucket == 0xffffffff)
+				bucket = 0;
+	}
+
+	static void record(std::int8_t celsius)
+	{
+		auto now = uptime::millis();
+		if (now >= last_sample + sample_delay_ms) {
+			++histogram[clamp(celsius)];
+			last_sample = now;
+		}
+		if (now >= last_writeback + writeback_delay_ms) {
+			save();
+			last_writeback = now;
+		}
+	}
+
+	static void save()
+	{
+		stored::update(histogram);
+	}
+
+	static void reset()
+	{
+		histogram = {};
+		stored::update(histogram);
+	}
+
+	static std::uint8_t min_temperature()
+	{
+		for (std::uint8_t i = 0; i < range; ++i)
+			if (histogram[i])
+				return i;
+		return range;
+	}
+
+	static std::uint8_t max_temperature()
+	{
+		for (std::uint8_t i = range; i > 0; --i)
+			if (histogram[i - 1])
+				return i - 1;
+		return 0;
+	}
+
+	static std::uint64_t total_samples()
+	{
+		std::uint64_t total = 0;
+		for (auto bucket : histogram)
+			total += bucket;
+		return total;
+	}
+
+	static std::uint32_t highest_bucket()
+	{
+		std::uint32_t highest = 0;
+		for (auto bucket : histogram)
+			if (bucket > highest)
+				highest = bucket;
+		return highest;
+	}
+
+	static std::uint32_t bucket(std::uint8_t celsius)
+	{
+		return histogram[clamp(static_cast<std::int8_t>(celsius))];
+	}
+};
+
+} // namespace app