2 files changed, 290 insertions, 0 deletions
diff --git a/sem4/embedded/emb_m2/emb_m2.ino b/sem4/embedded/emb_m2/emb_m2.ino
new file mode 100644
index 0000000..c6a6a07
--- /dev/null
+++ b/sem4/embedded/emb_m2/emb_m2.ino
@@ -0,0 +1,233 @@
+#include "myfloat_red.h"
+
+// Number of numbers
+#define NN 100
+#define PRINT_PRECISION 10
+
+#define NEXT_OPG(c) Serial.print("\nOpgave "); Serial.println(c++);
+#define AND_OPG(c) Serial.print("and "); Serial.println(c++);
+
+unsigned int opg_count = 1;
+
+void printmydoubarr(myfloat_type *arr, size_t len) {
+	Serial.print("[ ");
+	for(size_t i = 0; i < len; i++) {
+		Serial.print(myfloat2double( &arr[i] ), PRINT_PRECISION);
+		Serial.print(" ");
+	}
+	Serial.println("]");
+}
+
+void printarr(double *arr, size_t len) {
+	Serial.print("[ ");
+	for(size_t i = 0; i < len; i++) {
+		Serial.print(arr[i], PRINT_PRECISION);
+		Serial.print(" ");
+	}
+	Serial.println("]");
+}
+
+unsigned long factorial(unsigned int n) {
+	unsigned long res = 1;
+	for(unsigned int i = 2; i <= n; i++) {
+		res *= i;
+	}
+
+	return res;
+}
+
+double sineTayler(double x, unsigned int n) {
+	double sum = 0;
+
+	for(unsigned int i = 0; i <= n; i++) {
+		sum += ((double)pow(-1, i) / (double)factorial(2 * i + 1)) * (double)pow(x, 2 * i + 1);
+	}
+
+
+	return sum;
+}
+
+#define TAU 1.57079632679
+// After some trial and error the best TAYLORN was 2
+#define TAYLORN 2
+double sine(double x) {
+
+	// Works by finding value in specific -pi/2 to pi/2 period.
+	int period = x / TAU;
+
+	// One cycle of sin takes 4 periods.
+	// If 0 just return the sine approx x
+	// If 1 do negative sine approx on x - TAU
+	// If 2 do negative sine approx x
+	// If 3 do sine approx on period x - TAU
+	x = abs(x - TAU*period);
+
+	double res = 12;
+	
+	switch( abs(period % 4) ) {
+		case 0:
+			res = sineTayler(x, TAYLORN);
+			break;
+		case 1:
+			res = -sineTayler(x - TAU, TAYLORN);
+			break;
+		case 2:
+			res = -sineTayler(x, TAYLORN);
+			break;
+		case 3:
+			res = sineTayler(x - TAU, TAYLORN);
+			break;
+	}
+	// Remember to multiply with sign
+	int sign = period < 0 ? -1 : 1;
+
+	// Should never return because all cases are handled
+	return res * sign;
+
+}
+
+void mean_rel_error(double *da, myfloat_type *mda, size_t len, double *sign) {
+	// Calculate and print the relative error using the formula
+	//  X - x
+	//  -----   Where x is the calculated value and X is the real value( As real as double gets )
+	//    X
+	double errorsum = 0;
+	Serial.print("Rel Err : [ ");
+	for(size_t i = 0; i < len; i++) {
+		//Serial.println(errorsum, PRINT_PRECISION);
+		// Make space for sign
+		if( sign[i] < 0 ) {
+			Serial.print(" ");
+		}
+		// Handle devide by 0
+		double error = da[i] ? abs(da[i] - myfloat2double(&mda[i])) / abs(da[i]) : 0;
+		Serial.print(error, PRINT_PRECISION);
+		Serial.print(" ");
+
+		// Save sum for mean
+		errorsum += error;
+	}
+	Serial.println("]");
+
+	// Calculate mean
+	double mean = errorsum / len;
+	Serial.print("Mean Err: "); Serial.println(mean, PRINT_PRECISION);
+}
+
+void setup() {
+	Serial.begin(115200);
+
+	NEXT_OPG(opg_count);
+	// OPG1. Create some doubles 
+	double da[NN];
+	for(int i = 0; i < NN; i++) {
+		da[i] = ((double)random(-5000, 5000)) / 1000.0;
+	}
+	Serial.print("Original: "); printarr(da, NN);
+
+	NEXT_OPG(opg_count);
+	// OPG2. Convert to mda
+	myfloat_type mda[NN];
+	for(int i = 0; i < NN; i++) {
+		doub2mydouble(da[i], &mda[i]);
+	}
+
+	Serial.print("Mydoub  : "); printmydoubarr(mda, NN);
+
+	NEXT_OPG(opg_count);
+	// OPG3. Calculate the mean relative error
+	mean_rel_error(da, mda, NN, da);
+
+	{
+		NEXT_OPG(opg_count);
+		// OPG4. Compute some stuff
+		double da2[NN];
+		for(int i = 0; i < NN; i++) {
+			da2[i] = da[i] * da[i];
+		}
+		Serial.print("Orig pow: "); printarr(da2, NN);
+
+		NEXT_OPG(opg_count);
+		// OPG5.
+		myfloat_type mda2[NN];
+		for(int i = 0; i < NN; i++) {
+			// This thing sometimes does weird stuff -4.06*(-4.06) -> -16.00
+			mult_float(&mda[i], &mda[i], &mda2[i]);
+		}
+		Serial.print("Mda  pow: "); printmydoubarr(mda2, NN);
+
+		NEXT_OPG(opg_count);
+		// OPG6. Doing the mean error thing
+		mean_rel_error(da2, mda2, NN, da);
+	}
+
+	{
+		// OPG7. Measure execution time
+		NEXT_OPG(opg_count);
+		double a = da[1];
+		unsigned long begin = micros();
+		for(int i = 1; i < NN; i++) {
+			a *= da[i];
+		}
+
+		unsigned long time1 = micros() - begin;
+		Serial.print("Exe time: "); Serial.println(time1);
+		Serial.print("a       : "); Serial.println(a);
+
+		NEXT_OPG(opg_count);
+		// Convert to myfloat
+		myfloat_type f1;
+		doub2mydouble(a, &f1);
+
+		Serial.print("f1      : "); Serial.println(myfloat2double(&f1));
+
+		NEXT_OPG(opg_count);
+		// OPG8-9.
+		begin = micros();
+		for(int i = 0; i < NN; i++) {
+			// Multiply
+			myfloat_type f;
+			mult_float(&f1, &mda[i], &f);
+
+			// Copy back
+			memcpy(&f1, &f, sizeof(myfloat_type));
+		}
+
+		unsigned long time2 = micros() - begin;
+		Serial.print("Exe time: "); Serial.println(time2);
+		Serial.print("f1      : "); Serial.println(myfloat2double(&f1));
+		Serial.println("Overflow");
+
+		NEXT_OPG(opg_count);
+		// OPG10. Difference relative to biggest result
+
+		unsigned long absdiff = abs( time1 - time2 );
+		Serial.print("Abs diff: "); Serial.println(absdiff);
+		double reldiff = (double)absdiff / max(abs(time1), abs(time2));
+		Serial.print("Rel diff: "); Serial.println(reldiff);
+	}
+
+	NEXT_OPG(opg_count);
+	// OPG11. Impl sine
+	// Hardest value should be TAU as it's the furthest from center.
+	unsigned long begin = micros();
+	double res = sine(TAU);
+	unsigned long time1 = micros() - begin;
+	Serial.print("own sin : "); Serial.println(res, PRINT_PRECISION);
+
+	begin = micros();
+	double correct = sin(TAU);
+	unsigned long time2 = micros() - begin;
+	Serial.print("ard sin : "); Serial.println(correct, PRINT_PRECISION);
+
+	double error = correct ? abs(correct - res) / abs(correct) : 0;
+	Serial.print("rel err : "); Serial.println(error, PRINT_PRECISION);
+
+	Serial.print("\nown time: "); Serial.println(time1);
+	Serial.print("ard time: "); Serial.println(time2);
+
+}
+
+void loop() {
+
+}
diff --git a/sem4/embedded/emb_m2/myfloat_red.h b/sem4/embedded/emb_m2/myfloat_red.h
new file mode 100644
index 0000000..b553233
--- /dev/null
+++ b/sem4/embedded/emb_m2/myfloat_red.h
@@ -0,0 +1,57 @@
+/*
+  Low level precision floating point lib
+  Author: Henrik Schiøler
+*/
+
+//low precision floating pt type
+typedef struct myfloat
+{
+        signed char mantissa;
+        signed char exponent;
+} myfloat_type;
+
+
+//convert from double to low precision type
+void doub2mydouble(double arg, myfloat_type *res)
+{
+   int exponent;
+   double temp;
+   exponent = ceil(log(abs(arg))/log(2)); //base 2 logarithm
+   temp=arg*pow(2,7-exponent);
+   res->mantissa = (signed char)temp;
+   res->exponent = exponent-7;
+}
+
+//convert from low precision type to double
+double myfloat2double(myfloat_type *arg1)
+{
+  double res = (double)(arg1->mantissa) * pow(2,arg1->exponent);
+   return res;
+}
+
+//multiply to low precision types
+void mult_float(myfloat_type *arg1,myfloat_type *arg2,myfloat_type *result)
+{
+  int temp;
+  unsigned char sign;
+  
+  sign=0x80 & ((unsigned char)arg1-> mantissa ^ (unsigned char)arg2-> mantissa); //find sign of result 
+  
+  char i=0;
+   temp = (int)(arg1-> mantissa) * (int)(arg2-> mantissa);
+   
+   temp = temp & 0x7f00; //take away sign from product
+  
+   while(abs(temp)>128)
+   {
+      i++;
+      temp=temp>>1;
+   }
+   
+   result->mantissa = (unsigned char) temp;
+   
+   result->mantissa = result->mantissa | sign; //add recorded sign
+   
+   result->exponent = arg1->exponent + arg2->exponent + i;
+   
+}