ntpd: try to avoid using libm. -1.2k if we succeed

uclibc's sqrt(x) is pathetic, 411 bytes? it can be ~100...

Signed-off-by: Denys Vlasenko <vda.linux@googlemail.com>

diff --git a/networking/ntpd.c b/networking/ntpd.c
index 08e51ef..f147d8c 100644 (file)
--- a/networking/ntpd.c
+++ b/networking/ntpd.c
@@ -299,7 +299,45 @@ static ALWAYS_INLINE double MIND(double a, double b)
                return a;
        return b;
 }
-#define SQRT(x) (sqrt(x))
+static NOINLINE double my_SQRT(double X)
+{
+       union {
+               float   f;
+               int32_t i;
+       } v;
+       double invsqrt;
+       double Xhalf = X * 0.5;
+
+       /* Fast and good approximation to 1/sqrt(X), black magic */
+       v.f = X;
+       /*v.i = 0x5f3759df - (v.i >> 1);*/
+       v.i = 0x5f375a86 - (v.i >> 1); /* - this constant is slightly better */
+       invsqrt = v.f; /* better than 0.2% accuracy */
+
+       /* Refining it using Newton's method: x1 = x0 - f(x0)/f'(x0)
+        * f(x) = 1/(x*x) - X  (f==0 when x = 1/sqrt(X))
+        * f'(x) = -2/(x*x*x)
+        * f(x)/f'(x) = (X - 1/(x*x)) / (2/(x*x*x)) = X*x*x*x/2 - x/2
+        * x1 = x0 - (X*x0*x0*x0/2 - x0/2) = 1.5*x0 - X*x0*x0*x0/2 = x0*(1.5 - (X/2)*x0*x0)
+        */
+       invsqrt = invsqrt * (1.5 - Xhalf * invsqrt * invsqrt); /* ~0.05% accuracy */
+       /* invsqrt = invsqrt * (1.5 - Xhalf * invsqrt * invsqrt); 2nd iter: ~0.0001% accuracy */
+       /* With 4 iterations, more than half results will be exact,
+        * at 6th iterations result stabilizes with about 72% results exact.
+        * We are well satisfied with 0.05% accuracy.
+        */
+
+       return X * invsqrt; /* X * 1/sqrt(X) ~= sqrt(X) */
+}
+static ALWAYS_INLINE double SQRT(double X)
+{
+       /* If this arch doesn't use IEEE 754 floats, fall back to using libm */
+       if (sizeof(float) != 4)
+               return sqrt(X);
+
+       /* This avoids needing libm, saves about 1.2k on x86-32 */
+       return my_SQRT(X);
+}
 
 static double
 gettime1900d(void)