Import of the watch repository from Pebble

src/libutil/math.c

@@ -0,0 +1,95 @@
+/*
+ * Copyright 2024 Google LLC
+ *
+ * Licensed under the Apache License, Version 2.0 (the "License");
+ * you may not use this file except in compliance with the License.
+ * You may obtain a copy of the License at
+ *
+ *     http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ */
+
+#include "util/math.h"
+
+#include <stdint.h>
+#include <stdbool.h>
+
+int32_t sign_extend(uint32_t a, int bits) {
+  if (bits == 32) {
+    return a;
+  }
+
+  // http://graphics.stanford.edu/~seander/bithacks.html#VariableSignExtend
+  int const m = 1U << (bits - 1); // mask can be pre-computed if b is fixed
+
+  a = a & ((1U << bits) - 1);  // (Skip this if bits in x above position b are already zero.)
+  return (a ^ m) - m;
+}
+
+int32_t serial_distance32(uint32_t a, uint32_t b) {
+  return serial_distance(a, b, 32);
+}
+
+int32_t serial_distance(uint32_t a, uint32_t b, int bits) {
+  // See https://en.wikipedia.org/wiki/Serial_Number_Arithmetic
+  const int64_t a_minus_b = a - b;
+  const int64_t b_minus_a = b - a;
+  const bool a_is_earlier_than_b = (a < b && b_minus_a < (1 << (bits - 1))) || (a > b && a_minus_b > (1 << (bits - 1)));
+  return sign_extend(a_is_earlier_than_b ? -a_minus_b : b_minus_a, bits);
+}
+
+int ceil_log_two(uint32_t n) {
+    // clz stands for Count Leading Zeroes. We use it to find the MSB
+    int msb = 31 - __builtin_clz(n);
+    // popcount counts the number of set bits in a word (1's)
+    bool power_of_two = __builtin_popcount(n) == 1;
+    // if not exact power of two, use the next power of two
+    // we want to err on the side of caution and want to
+    // always round up
+    return ((power_of_two) ? msb : (msb + 1));
+}
+
+//! newton's method for floor(sqrt(x)) -> should always converge
+int32_t integer_sqrt(int64_t x) {
+  if (x < 0) {
+    return 0;
+  }
+  int64_t last_res = 0x3fff;
+  uint16_t iterations = 0;
+  while ((last_res > 0) && (iterations < 15)) {
+    last_res = ((x / last_res) + last_res)/2;
+    iterations++;
+  }
+  return (last_res);
+}
+
+uint32_t next_exponential_backoff(uint32_t *attempt, uint32_t initial_value, uint32_t max_value) {
+  if (*attempt > 31) {
+    return max_value;
+  }
+  uint32_t backoff_multiplier = 0x1 << (*attempt)++;
+  uint32_t next_value = initial_value * backoff_multiplier;
+  return MIN(next_value, max_value);
+}
+
+uint32_t gcd(uint32_t a, uint32_t b) {
+  // Infinite loops are bad
+  if (a == 0 || b == 0) {
+    return 0;
+  }
+
+  // Euclidean algorithm, yay!
+  while (a != b) {
+    if (a > b) {
+      a -= b;
+    } else {
+      b -= a;
+    }
+  }
+  return a;
+}