core: improve sin() and exp() performance by replacing divisions with

multiplications where appropriate.

src/real.cpp

@@ -668,13 +668,16 @@ static real fast_exp(real const &x)
 
     for (int i = 1; ; i++)
     {
-        fact *= (real)i;
-        real newret = ret + xn / fact;
+        real newret = ret + xn;
         if (newret == ret)
             break;
         ret = newret;
+        real mul = (i + 1);
+        fact *= mul;
+        ret *= mul;
         xn *= x;
     }
+    ret /= fact;
 
     return ret;
 }
@@ -802,16 +805,19 @@ real sin(real const &x)
     if (absx > real::R_PI_2)
         absx = real::R_PI - absx;
 
-    real ret = real::R_0, fact = real::R_1, xn = absx, x2 = absx * absx;
+    real ret = real::R_0, fact = real::R_1, xn = absx, mx2 = -absx * absx;
     for (int i = 1; ; i += 2)
     {
-        real newret = ret + xn / fact;
+        real newret = ret + xn;
         if (newret == ret)
             break;
         ret = newret;
-        xn *= x2;
-        fact *= (real)(-(i + 1) * (i + 2));
+        real mul = (i + 1) * (i + 2);
+        fact *= mul;
+        ret *= mul;
+        xn *= mx2;
     }
+    ret /= fact;
 
     /* Propagate sign */
     if (switch_sign)

test/benchmark/real.cpp

@@ -56,6 +56,16 @@ void bench_real(int mode)
         for (size_t i = 0; i < REAL_TABLE_SIZE; i++)
             invfact = invfact / real(1.0 + i);
         result[2] += timer.GetMs();
+
+        timer.GetMs();
+        for (size_t i = 0; i < REAL_TABLE_SIZE / 128; i++)
+            sin(real(0.01 * i));
+        result[3] += timer.GetMs() * 128;
+
+        timer.GetMs();
+        for (size_t i = 0; i < REAL_TABLE_SIZE / 128; i++)
+            exp((real)(int)(i - REAL_TABLE_SIZE / 256));
+        result[4] += timer.GetMs() * 128;
     }
 
     for (size_t i = 0; i < sizeof(result) / sizeof(*result); i++)
@@ -65,5 +75,7 @@ void bench_real(int mode)
     Log::Info("real = real + real           %7.3f\n", result[0]);
     Log::Info("real = real * real           %7.3f\n", result[1]);
     Log::Info("real = real / real           %7.3f\n", result[2]);
+    Log::Info("real = sin(real)             %7.3f\n", result[3]);
+    Log::Info("real = exp(real)             %7.3f\n", result[4]);
 }