initial exp() implementation

(refout for log(1.5) changed due to using more accurate expected result)

src/decn/proto/.gitignore

@@ -1,3 +1,4 @@
 div
 ln
+exp
 

src/decn/proto/Makefile

@@ -1,4 +1,4 @@
-all: div ln
+all: div ln exp
 
 div: div_mfp.cpp
 	g++ -Wall div_mfp.cpp -o div -lgmp
@@ -6,3 +6,5 @@ div: div_mfp.cpp
 ln: ln_mfp.cpp
 	g++ -Wall ln_mfp.cpp -o ln -lmpfr
 
+exp: exp.cpp
+	g++ -Wall exp.cpp -o exp -lmpfr

src/decn/proto/exp.cpp

@@ -0,0 +1,130 @@
+//prototype for exponential function
+// complement of ln() function based on HP Journal article
+// "Personal Calculator Algorithms IV: Logarithmic Functions"
+// (uses same set of constants)
+
+#include <stdio.h>
+#include <iostream>
+#include <math.h>
+#include <boost/multiprecision/mpfr.hpp>
+using namespace boost::multiprecision;
+
+// #define DEBUG
+// #define DEBUG_ALL
+
+using std::cout;
+using std::endl;
+
+static const int NUM_A_ARR = 9;
+mpfr_float a_arr[NUM_A_ARR];
+mpfr_float ln_a_arr[NUM_A_ARR];
+
+static const unsigned int CALC_PRECISION = 18;
+
+
+int main(void){
+	cout << std::scientific << std::setprecision(CALC_PRECISION);
+	mpfr_float ln10 (10, CALC_PRECISION);
+	ln10 = log( ln10 );
+	cout << "ln(10):" << ln10 << endl;
+	//initiallize a_arr and ln_a_arr
+	for (int i = 0; i < NUM_A_ARR; i++){
+		// a[i] = (1 + 10^-i)
+		mpfr_float a(-i, CALC_PRECISION);
+		a = pow(10, a);
+		a_arr[i] = a + 1;
+		ln_a_arr[i] = log(a_arr[i]);
+		cout << i << endl;
+		cout << "     a:" << a_arr[i] << endl;
+		cout << " ln(a):" << ln_a_arr[i] << endl;
+	}
+	cout << endl << endl ;
+	//loop through values to test
+	for (mpfr_float x(0.0001, CALC_PRECISION); x < 230.0; x += 0.015625){
+// 	for (mpfr_float x(230, CALC_PRECISION); x < 230.01; x += 0.015625){
+		//build mpf values
+		mpfr_float accum(x, CALC_PRECISION);
+		mpfr_float save (0, CALC_PRECISION);
+		mpfr_float_1000 actual;
+		actual = exp(x);
+
+		int num_times_ln10;
+		int num_times[NUM_A_ARR];
+		int k_j = 0;
+		//track number of times 10*ln(10) subtracted
+		while (accum > 0){
+			save = accum;
+			accum -= 10*ln10;
+			k_j++;
+		}
+		num_times_ln10 = (k_j - 1) * 10;
+		accum = save; //restore
+		//track number of times ln(10) subtracted
+		k_j = 0;
+		while (accum > 0){
+			save = accum;
+			accum -= ln10;
+			k_j++;
+		}
+		num_times_ln10 += k_j - 1;
+		accum = save; //restore
+#ifdef DEBUG
+		printf("  10: num_times: %d, ", num_times_ln10);
+		cout << accum << endl;
+#endif
+		//track number of times ln_a_arr[j] subtracted
+		for (int j = 0; j < NUM_A_ARR; j++){
+			k_j = 0;
+			while (accum > 0){
+				save = accum;
+				accum -= ln_a_arr[j];
+#ifdef DEBUG_ALL
+				printf("     %d: ", k_j);
+				cout << accum << endl;
+#endif
+				k_j++;
+			}
+			num_times[j] = k_j - 1;
+			accum = save; //restore
+#ifdef DEBUG
+			printf("  %d: num_times: %d, ", j, num_times[j]);
+			cout << accum << endl;
+#endif
+		}
+
+		//build final value
+		accum = 1+save; //initialize product to 1+remainder
+		//multiplies for ln(10)
+		for (int k = 0; k < num_times_ln10; k++){
+			accum *= 10;
+		}
+		//multiplies for ln(1 + 10^-j)
+		for (int j = 0; j < NUM_A_ARR; j++){
+			for (int k = 0; k < num_times[j]; k++){
+				accum *= a_arr[j];
+			}
+		}
+
+
+		//calculate relative error
+		mpfr_float_1000 calc, diff;
+		calc = accum;
+		diff = abs((actual - calc)/actual);
+
+#ifdef DEBUG_ALL
+		if (1){
+#else
+		if (diff > 5e-17){
+#endif
+			cout << x << ": ";
+			cout << std::setprecision(18) << accum << ", ";
+#ifdef DEBUG_ALL
+			cout << actual << ", ";
+#endif
+			cout << diff << endl;
+		}
+	}
+
+	return 0;
+}
+

src/decn/proto/ln_mfp.cpp

@@ -80,7 +80,7 @@ int main(void){
 		//calculate relative error
 		mpfr_float_1000 calc, diff;
 		calc = accum;
-		diff = (actual - calc)/actual;
+		diff = abs((actual - calc)/actual);
 
 		if (diff > 5e-17){
 			cout << x << ": ";