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