Refactor trig functions into LUT (#476)

Replaced the use of the standard library trig functions with a LUT-based
implementation instead. The standard library implementations produce
more accurate results but the usage here doesn't need that. This ends up
saving nearly 7kB of binary size.

Author: jvandermey-evertz

src/displayapp/screens/WatchFaceAnalog.cpp

@@ -5,27 +5,44 @@
 #include "Symbols.h"
 #include "NotificationIcon.h"
 
-#include <cmath>
-
 LV_IMG_DECLARE(bg_clock);
 
 using namespace Pinetime::Applications::Screens;
 
-#define HOUR_LENGTH   70
-#define MINUTE_LENGTH 90
-#define SECOND_LENGTH 110
-#define PI            3.14159265358979323846
+namespace {
+
+constexpr auto HOUR_LENGTH = 70;
+constexpr auto MINUTE_LENGTH = 90;
+constexpr auto SECOND_LENGTH = 110;
+
+// sin(90) = 1 so the value of _lv_trigo_sin(90) is the scaling factor
+const auto LV_TRIG_SCALE = _lv_trigo_sin(90);
+
+int16_t cosine(int16_t angle) {
+  return _lv_trigo_sin(angle + 90);
+}
+
+int16_t sine(int16_t angle) {
+  return _lv_trigo_sin(angle);
+}
+
+int16_t coordinate_x_relocate(int16_t x) {
+  return (x + LV_HOR_RES / 2);
+}
 
-// ##
-static int16_t coordinate_x_relocate(int16_t x) {
-  return ((x) + LV_HOR_RES / 2);
+int16_t coordinate_y_relocate(int16_t y) {
+  return std::abs(y - LV_HOR_RES / 2);
 }
 
-// ##
-static int16_t coordinate_y_relocate(int16_t y) {
-  return (((y) -LV_HOR_RES / 2) < 0) ? (0 - ((y) -LV_HOR_RES / 2)) : ((y) -LV_HOR_RES / 2);
+lv_point_t coordinate_relocate(int16_t radius, int16_t angle) {
+  return lv_point_t{
+    .x = coordinate_x_relocate(radius * static_cast<int32_t>(sine(angle)) / LV_TRIG_SCALE),
+    .y = coordinate_y_relocate(radius * static_cast<int32_t>(cosine(angle)) / LV_TRIG_SCALE)
+  };
 }
 
+} // namespace
+
 WatchFaceAnalog::WatchFaceAnalog(Pinetime::Applications::DisplayApp* app,
                                  Controllers::DateTime& dateTimeController,
                                  Controllers::Battery& batteryController,
@@ -123,15 +140,12 @@ void WatchFaceAnalog::UpdateClock() {
   second = dateTimeController.Seconds();
 
   if (sMinute != minute) {
-    minute_point[0].x = coordinate_x_relocate(30 * sin(minute * 6 * PI / 180));
-    minute_point[0].y = coordinate_y_relocate(30 * cos(minute * 6 * PI / 180));
-    minute_point[1].x = coordinate_x_relocate(MINUTE_LENGTH * sin(minute * 6 * PI / 180));
-    minute_point[1].y = coordinate_y_relocate(MINUTE_LENGTH * cos(minute * 6 * PI / 180));
+    auto const angle = minute * 6;
+    minute_point[0] = coordinate_relocate(30, angle);
+    minute_point[1] = coordinate_relocate(MINUTE_LENGTH, angle);
 
-    minute_point_trace[0].x = coordinate_x_relocate(5 * sin(minute * 6 * PI / 180));
-    minute_point_trace[0].y = coordinate_y_relocate(5 * cos(minute * 6 * PI / 180));
-    minute_point_trace[1].x = coordinate_x_relocate(31 * sin(minute * 6 * PI / 180));
-    minute_point_trace[1].y = coordinate_y_relocate(31 * cos(minute * 6 * PI / 180));
+    minute_point_trace[0] = coordinate_relocate(5, angle);
+    minute_point_trace[1] = coordinate_relocate(31, angle);
 
     lv_line_set_points(minute_body, minute_point, 2);
     lv_line_set_points(minute_body_trace, minute_point_trace, 2);
@@ -140,26 +154,24 @@ void WatchFaceAnalog::UpdateClock() {
   if (sHour != hour || sMinute != minute) {
     sHour = hour;
     sMinute = minute;
-    hour_point[0].x = coordinate_x_relocate(30 * sin((((hour > 12 ? hour - 12 : hour) * 30) + (minute * 0.5)) * PI / 180));
-    hour_point[0].y = coordinate_y_relocate(30 * cos((((hour > 12 ? hour - 12 : hour) * 30) + (minute * 0.5)) * PI / 180));
-    hour_point[1].x = coordinate_x_relocate(HOUR_LENGTH * sin((((hour > 12 ? hour - 12 : hour) * 30) + (minute * 0.5)) * PI / 180));
-    hour_point[1].y = coordinate_y_relocate(HOUR_LENGTH * cos((((hour > 12 ? hour - 12 : hour) * 30) + (minute * 0.5)) * PI / 180));
+    auto const angle = (hour * 30 + minute / 2);
+
+    hour_point[0] = coordinate_relocate(30, angle);
+    hour_point[1] = coordinate_relocate(HOUR_LENGTH, angle);
 
-    hour_point_trace[0].x = coordinate_x_relocate(5 * sin((((hour > 12 ? hour - 12 : hour) * 30) + (minute * 0.5)) * PI / 180));
-    hour_point_trace[0].y = coordinate_y_relocate(5 * cos((((hour > 12 ? hour - 12 : hour) * 30) + (minute * 0.5)) * PI / 180));
-    hour_point_trace[1].x = coordinate_x_relocate(31 * sin((((hour > 12 ? hour - 12 : hour) * 30) + (minute * 0.5)) * PI / 180));
-    hour_point_trace[1].y = coordinate_y_relocate(31 * cos((((hour > 12 ? hour - 12 : hour) * 30) + (minute * 0.5)) * PI / 180));
+    hour_point_trace[0] = coordinate_relocate(5, angle);
+    hour_point_trace[1] = coordinate_relocate(31, angle);
 
     lv_line_set_points(hour_body, hour_point, 2);
     lv_line_set_points(hour_body_trace, hour_point_trace, 2);
   }
 
   if (sSecond != second) {
     sSecond = second;
-    second_point[0].x = coordinate_x_relocate(20 * sin((180 + second * 6) * PI / 180));
-    second_point[0].y = coordinate_y_relocate(20 * cos((180 + second * 6) * PI / 180));
-    second_point[1].x = coordinate_x_relocate(SECOND_LENGTH * sin(second * 6 * PI / 180));
-    second_point[1].y = coordinate_y_relocate(SECOND_LENGTH * cos(second * 6 * PI / 180));
+    auto const angle = second * 6;
+
+    second_point[0] = coordinate_relocate(-20, angle);
+    second_point[1] = coordinate_relocate(SECOND_LENGTH, angle);
     lv_line_set_points(second_body, second_point, 2);
   }
 }