Merge pull request #18 from mooxmirror/master

Prepare for release v0.1.1

Author: Lennart

.travis.yml

@@ -1,6 +1,11 @@
 language: c
-compiler: clang
+compiler: g++-4.8
 sudo: required
+dist: trusty
+
+install:
+  - sudo apt-get update -qq
+  - sudo apt-get install gcc-4.8 -y -qq
 
 script:
   - make all

Makefile

@@ -1,25 +1,73 @@
 # Compiler flags
-CFLAGS=-I ./include -std=c++11 -Wall
-CFLAGS_LIB=-I ./include -std=c++11 -c
+CFLAGS=-I./include -std=gnu++11 -Wall
+CFLAGS_LIB=-I./include -std=gnu++11 -c
+CFLAGS_TEST=test/tmath_test.cpp build/libtmath.a
 
-all: lib
+all: lib test
+	@echo Done.
 
-lib: tmath.o
-	mkdir -p build
-	echo "Packaging library ..."
+lib: build_folder tmath.o
 	ar rcs build/libtmath.a build/tmath.o
 
-test: lib
-	echo "Running tests ..."
+test: test_sine test_cosine test_tangent test_cosecant test_cotangent test_secant test_rad_deg test_abs test_factorial test_roots test_power test_exp_log
+	@echo all tests passed
 
-examples: lib
-	echo "Building examples ..."
+build_folder:
+	@mkdir -p build
 
-tmath.o:
-	echo "Building source files ..."
-	mkdir -p build
+test_folder:
+	@mkdir -p build/test
+
+test_sine: test_folder
+	$(CC) $(CFLAGS) test/sine/test.cpp -o build/test/sine $(CFLAGS_TEST)
+	@build/test/sine
+
+test_cosine: test_folder
+	$(CC) $(CFLAGS) test/cosine/test.cpp -o build/test/cosine $(CFLAGS_TEST)
+	@build/test/cosine
+
+test_tangent: test_folder
+	$(CC) $(CFLAGS) test/tangent/test.cpp -o build/test/tangent $(CFLAGS_TEST)
+	@build/test/tangent
+
+test_cosecant: test_folder
+	$(CC) $(CFLAGS) test/cosecant/test.cpp -o build/test/cosecant $(CFLAGS_TEST)
+	@build/test/cosecant
+
+test_cotangent: test_folder
+	$(CC) $(CFLAGS) test/cotangent/test.cpp -o build/test/cotangent $(CFLAGS_TEST)
+	@build/test/cotangent
+
+test_secant: test_folder
+	$(CC) $(CFLAGS) test/secant/test.cpp -o build/test/secant $(CFLAGS_TEST)
+	@build/test/secant
+
+test_rad_deg: test_folder
+	$(CC) $(CFLAGS) test/rad-deg/test.cpp -o build/test/rad-deg $(CFLAGS_TEST)
+	@build/test/rad-deg
+
+test_abs: test_folder
+	$(CC) $(CFLAGS) test/abs/test.cpp -o build/test/abs $(CFLAGS_TEST)
+	@build/test/abs
+
+test_factorial: test_folder
+	$(CC) $(CFLAGS) test/factorial/test.cpp -o build/test/factorial $(CFLAGS_TEST)
+	@build/test/factorial
+
+test_roots: test_folder
+	$(CC) $(CFLAGS) test/roots/test.cpp -o build/test/roots $(CFLAGS_TEST)
+	@build/test/roots
+
+test_power: test_folder
+	$(CC) $(CFLAGS) test/power/test.cpp -o build/test/power $(CFLAGS_TEST)
+	@build/test/power
+
+test_exp_log: test_folder
+	$(CC) $(CFLAGS) test/exp-log/test.cpp -o build/test/exp-log $(CFLAGS_TEST)
+	@build/test/exp-log
+
+tmath.o: build_folder
 	$(CC) $(CFLAGS_LIB) src/tmath.cpp -o build/tmath.o
 
-clean:
-	echo "Cleaning up ..."
+clean: build_folder
 	rm build -f -r

README.md

@@ -3,7 +3,8 @@ A small math function collection based on the Taylor expansion series.
 
 ## Building the project
 - Download the source files from the `master`-tree
-- To build the project, you need to have `clang` and `make` installed
+- To build the project, you need to have `g++` and `make` installed
+- And you need to run `export CC=g++`
 - If everything is ready, run `make all` and ...
 - ... your `libtmath.a` library file is ready in the `build` folder
 
@@ -13,7 +14,7 @@ Just build it as described above, include the header files and link the library.
 ## What is included?
 
 Function                   | Description
-:------------------------: | -----------------------------------
+:------------------------: | ---------------------------------------
 `sin(DOUBLE x)`            | sine of x
 `asin(DOUBLE x)`           | arcsine of x
 `sinh(DOUBLE x)`           | hyperbolic sine of x
@@ -45,8 +46,12 @@ Function                   | Description
 `pow(LONG x, LONG n)`      | x to the power of n
 `pow(DOUBLE x, LONG n)`    | x to the power of n
 `fac(LONG n)`              | factorial of n
+`facd(LONG n)`             | factorial of n using floating point
+`oddfac(LONG n)`           | odd-factorial of n
+`oddfacd(LONG n)`          | odd-factorial of n using floating point
 `rad(DOUBLE x)`            | degrees to radiant
 `deg(DOUBLE x)`            | radiant to degrees
+`abs(DOUBLE x)`            | absolute value of x
 
 ## What is planned?
 - Statistics (planned for v0.3)

examples/arcsec_demo.cpp

@@ -31,7 +31,7 @@ DOUBLE sec(DOUBLE x);  // secant
 DOUBLE asec(DOUBLE x);  // arcsecant
 DOUBLE sech(DOUBLE x);  // hyperbolic secant
 
-DOUBLE cosec(DOUBLE x);  // cosecant
+DOUBLE csc(DOUBLE x);  // cosecant
 DOUBLE acsc(DOUBLE x);  // arccosecant
 DOUBLE csch(DOUBLE x);  // hyperbolic cosecant
 
@@ -51,6 +51,11 @@ DOUBLE pow(DOUBLE x, LONG n);
 LONG pow(LONG x, LONG n);
 
 LONG fac(LONG n);
+DOUBLE facd(LONG n);
+LONG oddfac(LONG n);
+DOUBLE oddfacd(LONG n);
+
+DOUBLE abs(DOUBLE x);
 }
 
 #endif

include/tmath.hpp

@@ -0,0 +1,14 @@
+#ifndef _TMATH_TEST_HPP
+#define _TMATH_TEST_HPP
+
+#include <string>
+#include "tmath.hpp"
+
+namespace TMathTest {
+const TMath::DOUBLE DEFAULT_TOLERANCE = 0.001;
+bool equal(TMath::DOUBLE x, TMath::DOUBLE y, TMath::DOUBLE tolerance);
+void assert(TMath::DOUBLE value, TMath::DOUBLE correct, std::string expression);
+void assert(TMath::DOUBLE value, TMath::DOUBLE correct, std::string expression, TMath::DOUBLE tolerance);
+}
+
+#endif

include/tmath_test.hpp

@@ -12,11 +12,17 @@ TMath::DOUBLE TMath::sin(DOUBLE x)
 }
 TMath::DOUBLE TMath::asin(DOUBLE x)
 {
-	x = mod(x + 1, 2) - 1;
 	DOUBLE r = 0;
-	for (LONG n = 0; n <= 8L; n++)
+	DOUBLE delta = 1;
+	for (LONG n = 1; delta > 1e-6; n++)
 	{
-		r += fac(2 * n) / (pow(DOUBLE(2), 2 * n) * pow(fac(n), 2) * (2 * n + 1)) * pow(x, 2 * n + 1);
+		LONG odd = 2 * n - 1;
+		DOUBLE oddf = oddfacd(odd - 2);
+		DOUBLE f = facd(odd);
+		DOUBLE p = pow(x, odd);
+		DOUBLE d = p / f * oddf * oddf;
+		delta = abs(d);
+		r += p / f * oddf * oddf;
 	}
 	return r;
 }
@@ -50,9 +56,13 @@ TMath::DOUBLE TMath::tan(DOUBLE x)
 TMath::DOUBLE TMath::atan(DOUBLE x)
 {
 	DOUBLE r = 0;
-	for (LONG n = 0; n <= 8; n++)
+	DOUBLE delta = 1;
+	for (LONG n = 0; delta > 1e-4; n++)
 	{
-		r += pow(DOUBLE(-1), n) * pow(x, 2 * n + 1) / (2 * n + 1);
+		LONG odd = 2 * n + 1;
+		DOUBLE d = DOUBLE(pow(-1LL, n)) * pow(x, odd) / DOUBLE(odd);
+		delta = abs(d);
+		r += d;
 	}
 	return r;
 }
@@ -87,7 +97,7 @@ TMath::DOUBLE TMath::sech(DOUBLE x)
 	return 1 / cosh(x);
 }
 /* ================================ COSECANT ======================================== */
-TMath::DOUBLE TMath::cosec(DOUBLE x)
+TMath::DOUBLE TMath::csc(DOUBLE x)
 {
 	return 1 / sin(x);
 }
@@ -133,7 +143,7 @@ TMath::DOUBLE TMath::exp(DOUBLE x)
 	DOUBLE r = 0;
 	for (LONG n = 0; n <= 15L; n++)
 	{
-		r += pow(x, n) / fac(n);
+		r += pow(x, n) / facd(n);
 	}
 	return r;
 }
@@ -208,6 +218,31 @@ TMath::LONG TMath::fac(LONG n) {
 	}
 	return r;
 }
+TMath::DOUBLE TMath::facd(LONG n) {
+	DOUBLE r = 1;
+	for (LONG i = 2; i <= n; i++) {
+		r *= DOUBLE(i);
+	}
+	return r;
+}
+TMath::LONG TMath::oddfac(LONG n) {
+	LONG r = 1;
+	for (LONG i = 3; i <= n; i += 2) {
+		r *= i;
+	}
+	return r;
+}
+TMath::DOUBLE TMath::oddfacd(LONG n) {
+	DOUBLE r = 1;
+	for (LONG i = 3; i <= n; i += 2) {
+		r *= DOUBLE(i);
+	}
+	return r;
+}
+TMath::DOUBLE TMath::abs(DOUBLE x) {
+	if (x < 0) return -x;
+	else return x;
+}
 /* ========================================== DEGREE / RADIANT CONVERSION ================================*/
 TMath::DOUBLE TMath::rad(DOUBLE deg)
 {

src/tmath.cpp

@@ -0,0 +1,17 @@
+/*
+   This test checks the abs function.
+ */
+
+#include "tmath.hpp"
+#include "tmath_test.hpp"
+
+int main(int argc, char const *argv[]) {
+	using TMathTest::assert;
+	using TMath::abs;
+
+	assert(abs(0.0), 0.0, "abs(0) == 0");
+    assert(abs(1.0), 1.0, "abs(1) == 1");
+    assert(abs(-1.0), 1.0, "abs(-1) == 1");
+
+	return 0;
+}

test/abs/test.cpp

@@ -0,0 +1,25 @@
+/*
+   This test checks the cosecant, arccosecant and hyperbolic cosecant function.
+ */
+
+#include "tmath.hpp"
+#include "tmath_test.hpp"
+
+int main(int argc, char const *argv[]) {
+	using TMathTest::assert;
+	using TMath::csc;
+	using TMath::acsc;
+	using TMath::csch;
+	using TMath::PI;
+
+	assert(csc(PI / 2.0), 1.0, "csc(PI/2) == 1");
+    assert(csc(-PI / 2.0), -1.0, "csc(-PI/2) == -1");
+
+	assert(acsc(1.1884), 1.0, "acsc(1.1884) == 1");
+    assert(acsc(-1.1884), -1.0, "acsc(-1.1884) == -1");
+
+	assert(csch(0.88137), 1.0, "csch(0.88137) == 1.0");
+    assert(csch(-0.88137), -1.0, "csch(-0.88137) == -1.0");
+
+	return 0;
+}

test/cosecant/test.cpp

@@ -0,0 +1,29 @@
+/*
+   This test checks the cosine, arccosine and hyperbolic cosine function.
+ */
+
+#include "tmath.hpp"
+#include "tmath_test.hpp"
+
+int main(int argc, char const *argv[]) {
+	using TMathTest::assert;
+	using TMath::cos;
+    using TMath::acos;
+    using TMath::cosh;
+    using TMath::PI;
+
+	assert(cos(0.0), 1, "cos(0) == 1");
+    assert(cos(PI/2.0), 0, "cos(PI/2) == 0");
+    assert(cos(PI), -1, "cos(PI) == -1");
+    assert(cos(PI * 1.5), 0, "cos(PI * 1.5) == 0");
+
+    assert(acos(0), PI * 0.5, "acos(0) == PI/2");
+    assert(acos(0.70711), PI * 0.25, "acos(1/sqrt(2)) == 1/4 PI");
+    assert(acos(-0.70711), PI * 0.75, "acos(1/sqrt(2)) == 3/4 PI");
+
+    assert(cosh(0), 1, "cosh(0) == 1");
+    assert(cosh(1.31696), 2, "cosh(1.31696) == 2");
+    assert(cosh(-1.31696), 2, "cosh(-1.31696) == 2");
+
+	return 0;
+}