sys: add header for integer division using multiplication / shifts

sys/include/div.h

+/*
+ * Copyright (C) 2015 Kaspar Schleiser <kaspar@schleiser.de>
+ *
+ * This file is subject to the terms and conditions of the GNU Lesser
+ * General Public License v2.1. See the file LICENSE in the top level
+ * directory for more details.
+ */
+
+/**
+ * @brief     Provides integer division functions
+ *
+ * This header provides some integer division functions that can be used
+ * to prevent linking in compiler-generated ones, which are often larger.
+ *
+ * @file
+ * @ingroup   sys_util
+ * @author  Kaspar Schleiser <kaspar@schleiser.de>
+ * @{
+ */
+
+#ifndef DIV_H
+#define DIV_H
+
+#include <assert.h>
+#include <stdint.h>
+
+#ifdef __cplusplus
+extern "C" {
+#endif
+
+/**
+ * @brief Integer divide val by 15625
+ *
+ * @pre val <= 16383999997
+ *
+ * @param[in]   val     dividend
+ * @return      (val / 15625)
+ */
+static inline uint64_t div_u64_by_15625(uint64_t val)
+{
+    /* a higher value would overflow 2^64 in the multiplication that follows */
+    assert(val <= 16383999997LLU);
+
+    return (val * 0x431bde83UL) >> (12 + 32);
+}
+
+/**
+ * @brief Integer divide val by 1000000
+ *
+ * @pre val <= 1048575999808
+ *
+ * @param[in]   val     dividend
+ * @return      (val / 1000000)
+ */
+static inline uint64_t div_u64_by_1000000(uint64_t val)
+{
+    /* a higher value would overflow 2^64 in the multiplication that follows */
+    assert(val <= 1048575999808LLU);
+
+    return div_u64_by_15625(val>>6);
+}
+
+/**
+ * @brief Divide val by (15625/512)
+ *
+ * This is used to quantize a 1MHz value to the closest 32768Hz value,
+ * e.g., for timers.
+ *
+ * The algorithm actually multiplies by 512 first, then divides by 15625,
+ * keeping the result closer to a floored floating point division.
+ *
+ * @param[in]   val     dividend
+ * @return      (val / (15625/512))
+ */
+static inline uint32_t div_u32_by_15625div512(uint32_t val)
+{
+    return ((uint64_t)(val) * 0x431bde83ul) >> (12 + 32 - 9);
+}
+
+/**
+ * @brief Integer divide val by 10
+ *
+ * @param[in]   n     dividend
+ * @return      (n / 10)
+ */
+static inline uint32_t div_u32_by_10(uint32_t n) {
+    uint32_t q, r;
+    q = (n >> 1) + (n >> 2);
+    q = q + (q >> 4);
+    q = q + (q >> 8);
+    q = q + (q >> 16);
+    q = q >> 3;
+    r = n - (((q << 2) + q) << 1);
+    return q + (r > 9);
+}
+
+/**
+ * @brief Modulo 10
+ *
+ * @param[in]   n     dividend
+ * @return      (n % 10)
+ */
+static inline uint32_t div_u32_mod_10(uint32_t n)
+{
+    return n - (div_u32_by_10(n)*10);
+}
+
+#ifdef __cplusplus
+}
+#endif
+/** @} */
+#endif /* DIV_H */