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

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

Signed-off-by: Denys Vlasenko <vda.linux@googlemail.com>
This commit is contained in:
Denys Vlasenko 2010-01-03 21:06:27 +01:00
parent 510f56aa6f
commit d498ff0ac4
1 changed files with 39 additions and 1 deletions
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40
networking/ntpd.c
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@ -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)