MCUdude
diff --git a/‎Arduino.h
+4-4 b/‎Arduino.h
+4-4
diff --git a/‎README.md
+75-1 b/‎README.md
+75-1
@@ -121,11 +121,11 @@ void yield(void);
 #undef abs
 #endif
 
-#define abs(x)       __builtin_abs(x)
+#define abs(x)       ({ typeof (x) _x = (x); _x > 0 ? _x : -x; })
 #define sq(x)        ({ typeof (x) _x = (x); _x * _x; })
-#define min(a,b)     ({ typeof (a) _a = (a); typeof (b) _b = (b); _a < _b ? _a : _b;    })
-#define max(a,b)     ({ typeof (a) _a = (a); typeof (b) _b = (b); _a > _b ? _a : _b;    })
-#define round(x)     ({ typeof (x) _x = (x); _x >= 0 ? (long)_x + 0.5 : (long)_x - 0.5; })
+#define min(a,b)     ({ typeof (a) _a = (a); typeof (b) _b = (b); _a < _b ? _a : _b; })
+#define max(a,b)     ({ typeof (a) _a = (a); typeof (b) _b = (b); _a > _b ? _a : _b; })
+#define round(x)     ({ typeof (x) _x = (x); _x >= 0 ? (long)(_x + 0.5) : (long)(_x - 0.5); })
 #define radians(deg) ((deg) * DEG_TO_RAD)
 #define degrees(rad) ((rad) * RAD_TO_DEG)
 #define constrain(x,low,high)     ({ \
 
@@ -3,28 +3,102 @@
 
 This repo contains the Arduino corefiles used with [MightyCore](https://github.com/MCUdude/MightyCore), [MegaCore](https://github.com/MCUdude/MegaCore), [MiniCore](https://github.com/MCUdude/MiniCore) and [MajorCore](https://github.com/MCUdude/MightyCore).
 
+
 ## Supported devices
+
 * ATmega640, ATmega1280, ATmega2560
 * ATmega64, ATmega128, ATmega1281, ATmega2561
 * AT90CAN32, AT90CAN64, AT90CAN128
 * ATmega8535, ATmega16, ATmega32, ATmega164A/P, ATmega324A/P/PA/PB, ATmega644/P, ATmega1284/P
 * ATmega8515, ATmega162
 * ATmega8, ATmega48/P/PA/PB, ATmega88/P/PA/PB, ATmega168/P/PA/PB, ATmega328/P/PA/PB
 
+
 ## Supported clock frequencies
-By supported I mean clocks that accurate timing is implemented for (millis, micros, delay, delayMicroseconds).
+
+By supported I mean clocks that accurate timing is implemented for (millis,
+micros, delay, delayMicroseconds).
+
 * 32 MHz
+* 25 MHz
 * 24 MHz
+* 22.1184 MHz
 * 20 MHz
 * 18.432 MHz
+* 18 MHz
+* 16.5 MHz
 * 16 MHz
 * 14.7456 MHz
 * 12 MHz
 * 11.0592 MHz
+* 10 MHz
+* 9.216 MHz
 * 8 MHz
 * 7.3728 MHz
+* 6 MHz
 * 4 MHz
 * 3.6864 MHz
 * 2 MHz
 * 1.8432 MHz
 * 1 MHz
+
+
+### Adding further clock frequencies
+
+The calculation of `millis()`, `micros()` and `delay()` is automatic for
+arbitrary frequencies.
+Depending on the prime factors of the frequency, it is either exact or
+approximate to 60 ppm accuracy (worst-case).
+The only thing required is adding support in `delayMicroseconds()`.
+
+
+### Exactness of `delayMicroseconds()`
+
+The `delayMicroseconds(unsigned int us)` implementation is exact up to a few
+cycles for the frequencies listed above.
+
+The maximum input parameter to work reliably is 10000 for 10 milliseconds.
+Its result is affected by interrupts occurring, which may prolong the delay.
+
+
+### Exactness of `micros()` and `delay()`
+
+For the clock speeds listed above, `micros()` is corrected to zero drift.
+Even for very long run times, the `micros()` function will precisely follow the
+oscillator used.
+
+Frequencies not listed above are either exact or corrected to below 60 ppm drift
+and in exact sync with `millis()`.
+
+Note that the result of `micros()` may jump up by several microseconds between
+consecutive calls and rolls over after one hour and eleven minutes.
+
+The `delay()` function uses `micros()` internally and inherits its drift accuracy
+with slight variations due to function call overhead and processing.
+It is immune to interrupts and thus long-term accurate.
+
+
+### Exactness of `millis()`
+
+For the clock speeds listed above, `millis()` is corrected to zero drift.
+Even for very long run times, the `millis()` function will precisely follow the
+oscillator used.
+
+Frequencies not listed above are either exact or corrected to below 60 ppm drift
+and in exact sync with `micros()` and `delay()`.
+
+We do not register the rollover of the `unsigned long` millis counter that
+occurs every 49.7 days; such would have to be done in the user's program.
+Often this is not necessary:  The code
+
+    if (millis() - millis_old >= interval) {
+      /* do something */
+      millis_old += interval;
+    }
+
+is long-term accurate even when rolling over provided `millis_old` is of type
+`unsigned long`.
+
+For clock speeds of 16 MHz and below, the return value of `millis()`
+occasionally jumps up by more than one (notwithstanding low/zero drift).
+Thus, when relying on consecutive returns, run at 16.5 MHz or higher.