core: add boolean operators on real numbers, add unit tests for that,

and simplify the Remez code accordingly.

src/real.cpp

@@ -442,6 +442,19 @@ bool real::operator >=(real const &x) const
     return !(*this < x);
 }
 
+bool real::operator !() const
+{
+    return !(bool)*this;
+}
+
+real::operator bool() const
+{
+    /* A real is "true" if it is non-zero (exponent is non-zero) AND
+     * not NaN (exponent is not full bits OR higher order mantissa is zero) */
+    uint32_t exponent = m_signexp << 1;
+    return exponent && (~exponent || m_mantissa[0] == 0);
+}
+
 real fres(real const &x)
 {
     if (!(x.m_signexp << 1))

src/real.h

@@ -58,6 +58,9 @@ public:
     bool operator <=(real const &x) const;
     bool operator >=(real const &x) const;
 
+    bool operator !() const;
+    operator bool() const;
+
     friend real fabs(real const &x);
 
     friend real fres(real const &x);

test/math/remez.cpp

@@ -21,30 +21,13 @@ using namespace lol;
 /* The order of the approximation we're looking for */
 static int const ORDER = 8;
 
-static real compute_pi()
-{
-    /* Approximate Pi using Machin's formula: 16*atan(1/5)-4*atan(1/239) */
-    real sum = 0.0, x0 = 5.0, x1 = 239.0;
-    real const m0 = -x0 * x0, m1 = -x1 * x1, r16 = 16.0, r4 = 4.0;
-
-    /* Degree 240 is required for 512-bit mantissa precision */
-    for (int i = 1; i < 240; i += 2)
-    {
-        sum += r16 / (x0 * (real)i) - r4 / (x1 * (real)i);
-        x0 *= m0;
-        x1 *= m1;
-    }
-    return sum;
-}
-
 /* The function we want to approximate */
 static real myfun(real const &x)
 {
-    static real const half_pi = compute_pi() * (real)0.5;
     static real const one = 1.0;
-    if (x == (real)0.0 || x == (real)-0.0)
-        return half_pi;
-    return sin(x * half_pi) / x;
+    if (!x)
+        return real::R_PI_2;
+    return sin(x * real::R_PI_2) / x;
     //return cos(x) - one;
     //return exp(x);
 }

test/unit/real.cpp

@@ -176,6 +176,23 @@ LOLUNIT_FIXTURE(RealTest)
         LOLUNIT_ASSERT_EQUAL((double)(a3 << 7), 0.0);
         LOLUNIT_ASSERT_EQUAL((double)(a3 << -7), 0.0);
     }
+
+    LOLUNIT_TEST(Bool)
+    {
+        real a = 0.0;
+        LOLUNIT_ASSERT(!a);
+
+        a = -0.0;
+        LOLUNIT_ASSERT(!a);
+
+        a = 1234.0;
+        LOLUNIT_ASSERT(a);
+        LOLUNIT_ASSERT(!!a);
+
+        a = -1234.0;
+        LOLUNIT_ASSERT(a);
+        LOLUNIT_ASSERT(!!a);
+    }
 };
 
 } /* namespace lol */