sys: util: Add gcd and lcm utilities

Add helpers to compute Greates Common Divisor (GCD) and Least Common
Multiple (LCM).

Signed-off-by: Phi Bang Nguyen <[email protected]>
Signed-off-by: Trung Hieu Le <[email protected]>

Author: ngphibang

include/zephyr/sys/util.h

@@ -1038,6 +1038,84 @@ static inline size_t sys_count_bits(const void *value, size_t len)
  */
 #define SIGN(x) (((x) > 0) - ((x) < 0))
 
+/**
+ * @brief Compute the Greatest Common Divisor (GCD) of two integers
+ * using the Euclidean algorithm.
+ *
+ * @param a First integer
+ * @param b Second integer
+ *
+ * @return The greatest common divisor of a and b, always returns an unsigned value.
+ *         If one of the parameters is 0, returns the absolute value of the other parameter.
+ */
+#define gcd(a, b) \
+	_Generic((a), \
+		int8_t : gcd_s, \
+		int16_t : gcd_s, \
+		int32_t : gcd_s, \
+		uint8_t : gcd_u, \
+		uint16_t : gcd_u, \
+		uint32_t : gcd_u)(a, b)
+
+static ALWAYS_INLINE uint32_t gcd_u(uint32_t a, uint32_t b)
+{
+	uint32_t c;
+
+	if (a == 0) {
+		return b;
+	}
+
+	if (b == 0) {
+		return a;
+	}
+
+	c = a % b;
+	while (c != 0) {
+		a = b;
+		b = c;
+		c = a % b;
+	}
+
+	return b;
+}
+
+static ALWAYS_INLINE uint32_t gcd_s(int32_t a, int32_t b)
+{
+	return gcd_u(a < 0 ? -a : a, b < 0 ? -b : b);
+}
+
+/**
+ * @brief Compute the Least Common Multiple (LCM) of two integers.
+ *
+ * @param a First integer
+ * @param b Second integer
+ *
+ * @retval The least common multiple of a and b.
+ * @retval 0 if either input is 0.
+ */
+#define lcm(a, b) \
+	_Generic((a), \
+		int8_t : lcm_s, \
+		int16_t : lcm_s, \
+		int32_t : lcm_s, \
+		uint8_t : lcm_u, \
+		uint16_t : lcm_u, \
+		uint32_t : lcm_u)(a, b)
+
+static ALWAYS_INLINE uint64_t lcm_u(uint32_t a, uint32_t b)
+{
+	if (a == 0 || b == 0) {
+		return 0;
+	}
+
+	return (uint64_t)(a / gcd_u(a, b)) * (uint64_t)b;
+}
+
+static ALWAYS_INLINE uint64_t lcm_s(int32_t a, int32_t b)
+{
+	return lcm_u(a < 0 ? -a : a, b < 0 ? -b : b);
+}
+
 #ifdef __cplusplus
 }
 #endif

tests/unit/util/main.c

@@ -1209,4 +1209,57 @@ ZTEST(util, test_bitmask_find_gap)
 	test_single_bitmask_find_gap(0x0000000F, 2, 6, false, 4, __LINE__);
 }
 
+ZTEST(util, test_gcd)
+{
+	/* Zero cases */
+	zassert_equal(gcd(0, 0), 0, "should be 0");
+	zassert_equal(gcd(0, INT_MAX), INT_MAX, "should be 0");
+	zassert_equal(gcd(INT_MAX, 0), INT_MAX, "should be 0");
+
+	/* normal cases */
+	zassert_equal(gcd(12, 8), 4, "should be 4");
+
+	/* Negative number cases */
+	zassert_equal(gcd(-12, 8), 4, "should be 4");
+	zassert_equal(gcd(-12, -8), 4, "should be 4");
+
+	/* prime numbers */
+	zassert_equal(gcd(17, 13), 1, "should be 1");
+	zassert_equal(gcd(25, 49), 1, "should be 1");
+
+	/* Boundary values */
+	zassert_equal(gcd(INT_MAX, INT_MAX), INT_MAX, "should be INT_MAX");
+	zassert_equal(gcd(INT_MIN, INT_MIN), (uint32_t)(-(int64_t)INT_MIN), "should be INT_MAX + 1");
+	zassert_equal(gcd(INT_MIN, INT_MAX), 1, "should be 1");
+	zassert_equal(gcd(UINT32_MAX, UINT32_MAX), UINT32_MAX, "should be UINT32_MAX");
+}
+
+ZTEST(util, test_lcm)
+{
+	/* Zero cases - lcm with 0 should be 0 */
+	zassert_equal(lcm(0, 0), 0, "should be 0");
+	zassert_equal(lcm(0, INT_MAX), 0, "should be 0");
+
+	/* Normal cases */
+	zassert_equal(lcm(12, 8), 24, "should be 24");
+	zassert_equal(lcm(8, 12), 24, "should be 24");
+
+	/* Negative number cases - lcm should always be positive */
+	zassert_equal(lcm(-12, 8), 24, "should be 24");
+
+	/* Prime numbers (gcd = 1, so lcm = a * b) */
+	zassert_equal(lcm(17, 13), 221, "should be 221");
+
+	/* Boundary values */
+	zassert_equal(lcm(INT_MAX, INT_MAX - 1), (uint64_t)INT_MAX * (INT_MAX - 1),
+		      "should be INT_MAX * (INT_MAX - 1)");
+	zassert_equal(lcm(INT_MIN, INT_MIN), (uint64_t)INT_MAX + 1,
+		      "should be INT_MIN");
+	zassert_equal(lcm(INT_MIN, INT_MAX),
+		      (uint64_t)INT_MAX * (uint64_t)(-(int64_t)INT_MIN),
+		      "should be INT_MAX * (INT_MAX + 1)");
+	zassert_equal(lcm(UINT32_MAX, UINT32_MAX), UINT32_MAX,
+		      "should be UINT32_MAX");
+}
+
 ZTEST_SUITE(util, NULL, NULL, NULL, NULL, NULL);