By Long Luo

挖坑!

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@HotSpotIntrinsicCandidate
public static double sin(double a) {
return StrictMath.sin(a);
}
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public static native double sin(double a);
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#ifndef __FDLIBM_H__
#include "fdlibm.h"
#endif

double __kernel_sin(double x, double y, int iy)
{
double z, r, v;
int32_t ix;

static const double half = 5.00000000000000000000e-01;
static const double S1 = -1.66666666666666324348e-01;
static const double S2 = 8.33333333332248946124e-03;
static const double S3 = -1.98412698298579493134e-04;
static const double S4 = 2.75573137070700676789e-06;
static const double S5 = -2.50507602534068634195e-08;
static const double S6 = 1.58969099521155010221e-10;

GET_HIGH_WORD(ix, x);
ix &= IC(0x7fffffff);
if (ix < IC(0x3e400000))
{
if ((int32_t) x == 0)
return x;
}
z = x * x;
v = z * x;
r = S2 + z * (S3 + z * (S4 + z * (S5 + z * S6)));
if (iy == 0)
return x + v * (S1 + z * r);
else
return x - ((z * (half * y - v * r) - y) - v * S1);
}

\[ \sin (x_0 + \Delta x) \approx \sin (x_0) + \sin'(x_0) \frac {\Delta x}{1!} + \sin''(x_0) \frac { \Delta x^2}{2!} + \sin'''(x_0) \frac {\Delta x^3}{3!} + \cdots \]

参考文献

  1. C mathematical functions
  2. Sine and cosine