motioncontroller: Add functions for analysis

These are functions for converting acceleration due to gravity to angles
in degrees, and some statistical analysis including the mean and
variance.

src/utility/Math.cpp

@@ -0,0 +1,49 @@
+#include "utility/Math.h"
+
+#include <lvgl/src/lv_misc/lv_math.h>
+
+using namespace Pinetime::Utility;
+
+#ifndef PINETIME_IS_RECOVERY
+
+int16_t Pinetime::Utility::Asin(int16_t arg) {
+  int16_t a = arg < 0 ? -arg : arg;
+
+  int16_t angle = 45;
+  int16_t low = 0;
+  int16_t high = 90;
+  while (low <= high) {
+    int16_t sinAngle = _lv_trigo_sin(angle);
+    int16_t sinAngleSub = _lv_trigo_sin(angle - 1);
+    int16_t sinAngleAdd = _lv_trigo_sin(angle + 1);
+
+    if (a >= sinAngleSub && a <= sinAngleAdd) {
+      if (a <= (sinAngleSub + sinAngle) / 2) {
+        angle--;
+      } else if (a > (sinAngle + sinAngleAdd) / 2) {
+        angle++;
+      }
+      break;
+    }
+
+    if (a < sinAngle) {
+      high = angle - 1;
+    }
+
+    else {
+      low = angle + 1;
+    }
+
+    angle = (low + high) / 2;
+  }
+
+  return arg < 0 ? -angle : angle;
+}
+
+#else
+
+int16_t Pinetime::Utility::Asin(int16_t /*arg*/) {
+  return 0;
+}
+
+#endif

src/utility/Math.h

@@ -0,0 +1,10 @@
+#pragma once
+
+#include <cstdint>
+
+namespace Pinetime {
+  namespace Utility {
+    // returns the arcsin of `arg`. asin(-32767) = -90, asin(32767) = 90
+    int16_t Asin(int16_t arg);
+  }
+}