[math] Fix crc8_ccitt discarding the MSB of every input byte

The non-AVR path transliterates the avr-libc inline assembly literally:

    1:  lsl    %0        ; shift left, MSB -> CARRY
        brcc   2f        ; branch on CARRY, i.e. the *pre-shift* MSB
        eor    %0, %2

`lsl` preserves the departing bit in the carry flag, so `brcc` tests bit 7
of the value before the shift. C has no carry flag: `data <<= 1` on a
uint8_t discards that bit, so the following `if (data & 0x80)` tests the
pre-shift bit 6 instead and bit 7 is never examined.

Over all 32768 (crc, data) pairs this made

    crc8_ccitt_update(crc, data) == crc8_ccitt_update(crc, data ^ 0x80)

hold universally, left only 128 of 256 output values reachable, and made
single-bit errors in bit 7 of any byte undetectable.

Adds crc_test, which the module picks up by glob. There were no tests for
this header, which is why the fault went unnoticed; the new suite pins the
published check values for all three functions and asserts that flipping
the MSB of an input byte changes the CRC-8.

Author: TudorFanaru18

src/modm/math/utils/crc.hpp

@@ -31,8 +31,9 @@ crc8_ccitt_update(uint8_t crc, uint8_t data)
     data ^= crc;
     for (uint8_t ii = 0; ii < 8; ii++)
     {
+        const bool msb = (data & 0x80) != 0;
         data <<= 1;
-        if (data & 0x80) data ^= 0x07;
+        if (msb) data ^= 0x07;
     }
     return data;
 #endif

test/modm/math/utils/crc_test.cpp

@@ -0,0 +1,61 @@
+/*
+ * Copyright (c) 2026, Tudor Fanaru
+ *
+ * This file is part of the modm project.
+ *
+ * This Source Code Form is subject to the terms of the Mozilla Public
+ * License, v. 2.0. If a copy of the MPL was not distributed with this
+ * file, You can obtain one at http://mozilla.org/MPL/2.0/.
+ */
+// ----------------------------------------------------------------------------
+
+#include <modm/math/utils/crc.hpp>
+
+#include "crc_test.hpp"
+
+namespace
+{
+	// "123456789" is the input the CRC catalogue publishes check values against,
+	// so the expectations below are external references.
+	const uint8_t check_input[9] = {'1', '2', '3', '4', '5', '6', '7', '8', '9'};
+}
+
+void
+CrcTest::testCrc8CcittCheckValue()
+{
+	// CRC-8 with polynomial 0x07 and init 0xFF.
+	TEST_ASSERT_EQUALS(modm::math::crc8_ccitt(check_input, sizeof(check_input)), 0xFBU);
+}
+
+void
+CrcTest::testCrc8CcittUsesEveryInputBit()
+{
+	// Regression: shifting before testing bit 7 discards it, leaving the MSB of
+	// every input byte unexamined. That made crc8_ccitt_update(crc, d) equal
+	// crc8_ccitt_update(crc, d ^ 0x80) for all 32768 (crc, d) pairs, put only
+	// 128 of 256 outputs in reach, and left single-bit errors in that position
+	// undetectable.
+	for (uint16_t crc = 0; crc < 256; ++crc)
+	{
+		for (uint16_t data = 0; data < 128; ++data)
+		{
+			const uint8_t a = modm::math::crc8_ccitt_update(uint8_t(crc), uint8_t(data));
+			const uint8_t b = modm::math::crc8_ccitt_update(uint8_t(crc), uint8_t(data ^ 0x80));
+			TEST_ASSERT_TRUE(a != b);
+		}
+	}
+}
+
+void
+CrcTest::testCrc16CcittCheckValue()
+{
+	// CRC-16/MCRF4XX: reflected polynomial 0x8408, init 0xFFFF, no final xor.
+	TEST_ASSERT_EQUALS(modm::math::crc16_ccitt(check_input, sizeof(check_input)), 0x6F91U);
+}
+
+void
+CrcTest::testCrc32CheckValue()
+{
+	// CRC-32/ISO-HDLC, as used by zlib and PNG.
+	TEST_ASSERT_EQUALS(modm::math::crc32(check_input, sizeof(check_input)), 0xCBF43926UL);
+}

test/modm/math/utils/crc_test.hpp

@@ -0,0 +1,29 @@
+/*
+ * Copyright (c) 2026, Tudor Fanaru
+ *
+ * This file is part of the modm project.
+ *
+ * This Source Code Form is subject to the terms of the Mozilla Public
+ * License, v. 2.0. If a copy of the MPL was not distributed with this
+ * file, You can obtain one at http://mozilla.org/MPL/2.0/.
+ */
+// ----------------------------------------------------------------------------
+
+#include <unittest/testsuite.hpp>
+
+/// @ingroup modm_test_test_math
+class CrcTest : public unittest::TestSuite
+{
+public:
+	void
+	testCrc8CcittCheckValue();
+
+	void
+	testCrc8CcittUsesEveryInputBit();
+
+	void
+	testCrc16CcittCheckValue();
+
+	void
+	testCrc32CheckValue();
+};