core: add real constants for 0, 1, 2 and 10, and reorder static constants

so that their initialisation order ensures they have the proper values. Add
unit tests for these constants.

src/real.cpp

@@ -323,7 +323,7 @@ real real::operator *(real const &x) const
 
 real real::operator /(real const &x) const
 {
-    return *this * fres(x);
+    return *this * re(x);
 }
 
 real &real::operator +=(real const &x)
@@ -455,7 +455,7 @@ real::operator bool() const
     return exponent && (~exponent || m_mantissa[0] == 0);
 }
 
-real fres(real const &x)
+real re(real const &x)
 {
     if (!(x.m_signexp << 1))
     {
@@ -741,18 +741,23 @@ static real fast_pi()
     return ret;
 }
 
-real const real::R_E        = exp((real)1.0);
-real const real::R_LOG2E    = (real)1.0 / R_LN2;
-real const real::R_LOG10E   = (real)1.0 / R_LN10;
-real const real::R_LN2      = log((real)2.0);
-real const real::R_LN10     = log((real)10.0);
+real const real::R_0        = (real)0.0;
+real const real::R_1        = (real)1.0;
+real const real::R_2        = (real)2.0;
+real const real::R_10       = (real)10.0;
+
+real const real::R_E        = exp(R_1);
+real const real::R_LN2      = log(R_2);
+real const real::R_LN10     = log(R_10);
+real const real::R_LOG2E    = re(R_LN2);
+real const real::R_LOG10E   = re(R_LN10);
 real const real::R_PI       = fast_pi();
 real const real::R_PI_2     = R_PI >> 1;
 real const real::R_PI_4     = R_PI >> 2;
-real const real::R_1_PI     = (real)1.0 / R_PI;
+real const real::R_1_PI     = re(R_PI);
 real const real::R_2_PI     = R_1_PI << 1;
-real const real::R_2_SQRTPI = (real)2.0 / sqrt(R_PI);
-real const real::R_SQRT2    = sqrt((real)2.0);
+real const real::R_2_SQRTPI = re(sqrt(R_PI)) << 1;
+real const real::R_SQRT2    = sqrt(R_2);
 real const real::R_SQRT1_2  = R_SQRT2 >> 1;
 
 } /* namespace lol */

src/real.h

@@ -63,7 +63,7 @@ public:
 
     friend real fabs(real const &x);
 
-    friend real fres(real const &x);
+    friend real re(real const &x);
     friend real sqrt(real const &x);
     friend real log(real const &x);
     friend real exp(real const &x);
@@ -73,6 +73,11 @@ public:
 
     void print(int ndigits = 150) const;
 
+    static real const R_0;
+    static real const R_1;
+    static real const R_2;
+    static real const R_10;
+
     static real const R_E;
     static real const R_LOG2E;
     static real const R_LOG10E;

test/unit/real.cpp

@@ -22,6 +22,49 @@ namespace lol
 
 LOLUNIT_FIXTURE(RealTest)
 {
+    LOLUNIT_TEST(Constants)
+    {
+        double a0 = real::R_0;
+        double a1 = real::R_1;
+        double a2 = real::R_2;
+        double a10 = real::R_10;
+
+        LOLUNIT_ASSERT_EQUAL(a0, 0.0);
+        LOLUNIT_ASSERT_EQUAL(a1, 1.0);
+        LOLUNIT_ASSERT_EQUAL(a2, 2.0);
+        LOLUNIT_ASSERT_EQUAL(a10, 10.0);
+
+        double b0 = log(real::R_E);
+        LOLUNIT_ASSERT_EQUAL(b0, 1.0);
+
+        double b1 = exp(re(real::R_LOG2E));
+        LOLUNIT_ASSERT_EQUAL(b1, 2.0);
+
+        double b2 = exp(re(real::R_LOG10E));
+        LOLUNIT_ASSERT_EQUAL(b2, 10.0);
+
+        double b3 = exp(real::R_LN2);
+        LOLUNIT_ASSERT_EQUAL(b3, 2.0);
+
+        double b4 = exp(real::R_LN10);
+        LOLUNIT_ASSERT_EQUAL(b4, 10.0);
+
+        double b5 = sin(real::R_PI);
+        double b6 = cos(real::R_PI);
+        LOLUNIT_ASSERT_DOUBLES_EQUAL(b5, 0.0, 1e-100);
+        LOLUNIT_ASSERT_EQUAL(b6, -1.0);
+
+        double b7 = sin(real::R_PI_2);
+        double b8 = cos(real::R_PI_2);
+        LOLUNIT_ASSERT_EQUAL(b7, 1.0);
+        LOLUNIT_ASSERT_DOUBLES_EQUAL(b8, 0.0, 1e-100);
+
+        double b9 = sin(real::R_PI_4) * sin(real::R_PI_4);
+        double b10 = cos(real::R_PI_4) * cos(real::R_PI_4);
+        LOLUNIT_ASSERT_EQUAL(b9, 0.5);
+        LOLUNIT_ASSERT_EQUAL(b10, 0.5);
+    }
+
     LOLUNIT_TEST(FloatToReal)
     {
         float a1 = real(0.0f);