LibM: Implement various trig functions

Patch from Anonymous.

Libraries/LibM/math.cpp

@@ -1,10 +1,21 @@
 #include <LibC/assert.h>
 #include <LibM/math.h>
+#include <limits>
+#include <stdint.h>
+#include <stdlib.h>
+
+template<size_t> constexpr double e_to_power();
+template<> constexpr double e_to_power<0>() { return 1; }
+template<size_t exponent> constexpr double e_to_power() { return M_E * e_to_power<exponent - 1>(); }
+
+template<size_t> constexpr size_t factorial();
+template<> constexpr size_t factorial<0>() { return 1; }
+template<size_t value> constexpr size_t factorial() { return value * factorial<value - 1>(); }
 
 extern "C" {
 double trunc(double x)
 {
-    return (int)x;
+    return (int64_t)x;
 }
 
 double cos(double angle)
@@ -40,17 +51,25 @@ double pow(double x, double y)
     (void)x;
     (void)y;
     ASSERT_NOT_REACHED();
+    return 0;
 }
 
 double ldexp(double, int exp)
 {
     (void)exp;
     ASSERT_NOT_REACHED();
+    return 0;
 }
 
-double tanh(double)
+double tanh(double x)
 {
-    ASSERT_NOT_REACHED();
+    if (x > 0) {
+        double exponentiated = exp(2 * x);
+        return (exponentiated - 1) / (exponentiated + 1);
+    }
+    double plusX = exp(x);
+    double minusX = exp(-x);
+    return (plusX - minusX) / (plusX + minusX);
 }
 
 double tan(double angle)
@@ -65,19 +84,25 @@ double sqrt(double x)
     return res;
 }
 
-double sinh(double)
+double sinh(double x)
 {
-    ASSERT_NOT_REACHED();
+    if (x > 0) {
+        double exponentiated = exp(x);
+        return (exponentiated * exponentiated - 1) / 2 / exponentiated;
+    }
+    return (exp(x) - exp(-x)) / 2;
 }
 
 double log10(double)
 {
     ASSERT_NOT_REACHED();
+    return 0;
 }
 
 double log(double)
 {
     ASSERT_NOT_REACHED();
+    return 0;
 }
 
 double fmod(double index, double period)
@@ -85,67 +110,107 @@ double fmod(double index, double period)
     return index - trunc(index / period) * period;
 }
 
-double exp(double)
+double exp(double exponent)
 {
-    ASSERT_NOT_REACHED();
+    double result = 1;
+    if (exponent >= 1) {
+        size_t integer_part = (size_t)exponent;
+        if (integer_part & 1) result *= e_to_power<1>();
+        if (integer_part & 2) result *= e_to_power<2>();
+        if (integer_part > 3) {
+            if (integer_part & 4) result *= e_to_power<4>();
+            if (integer_part & 8) result *= e_to_power<8>();
+            if (integer_part & 16) result *= e_to_power<16>();
+            if (integer_part & 32) result *= e_to_power<32>();
+            if (integer_part >= 64) return std::numeric_limits<double>::infinity();
+        }
+        exponent -= integer_part;
+    } else if (exponent < 0)
+        return 1 / exp(-exponent);
+    double taylor_series_result = 1 + exponent;
+    double taylor_series_numerator = exponent * exponent;
+    taylor_series_result += taylor_series_numerator / factorial<2>();
+    taylor_series_numerator *= exponent;
+    taylor_series_result += taylor_series_numerator / factorial<3>();
+    taylor_series_numerator *= exponent;
+    taylor_series_result += taylor_series_numerator / factorial<4>();
+    taylor_series_numerator *= exponent;
+    taylor_series_result += taylor_series_numerator / factorial<5>();
+    return result * taylor_series_result;
 }
 
-double cosh(double)
+double cosh(double x)
 {
-    ASSERT_NOT_REACHED();
+    if (x < 0) {
+        double exponentiated = exp(-x);
+        return (1 + exponentiated * exponentiated) / 2 / exponentiated;
+    }
+    return (exp(x) + exp(-x)) / 2;
 }
 
 double atan2(double, double)
 {
     ASSERT_NOT_REACHED();
+    return 0;
 }
 
 double atan(double)
 {
     ASSERT_NOT_REACHED();
+    return 0;
 }
 
 double asin(double)
 {
     ASSERT_NOT_REACHED();
+    return 0;
 }
 
 double acos(double)
 {
     ASSERT_NOT_REACHED();
+    return 0;
 }
 
 double fabs(double value)
 {
     return value < 0 ? -value : value;
 }
+
 double log2(double)
 {
     ASSERT_NOT_REACHED();
+    return 0;
 }
 
 float log2f(float)
 {
     ASSERT_NOT_REACHED();
+    return 0;
 }
 
 long double log2l(long double)
 {
     ASSERT_NOT_REACHED();
+    return 0;
 }
 
 double frexp(double, int*)
 {
     ASSERT_NOT_REACHED();
+    return 0;
 }
 
 float frexpf(float, int*)
 {
     ASSERT_NOT_REACHED();
+    return 0;
 }
 
 long double frexpl(long double, int*)
 {
     ASSERT_NOT_REACHED();
+    return 0;
 }
+
 }