83 lines
2.2 KiB
C
83 lines
2.2 KiB
C
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#include "math.h"
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#include "math_private.h"
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static const double xxx[] = {
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3.33333333333334091986e-01, /* 3FD55555, 55555563 */
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1.33333333333201242699e-01, /* 3FC11111, 1110FE7A */
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5.39682539762260521377e-02, /* 3FABA1BA, 1BB341FE */
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2.18694882948595424599e-02, /* 3F9664F4, 8406D637 */
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8.86323982359930005737e-03, /* 3F8226E3, E96E8493 */
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3.59207910759131235356e-03, /* 3F6D6D22, C9560328 */
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1.45620945432529025516e-03, /* 3F57DBC8, FEE08315 */
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5.88041240820264096874e-04, /* 3F4344D8, F2F26501 */
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2.46463134818469906812e-04, /* 3F3026F7, 1A8D1068 */
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7.81794442939557092300e-05, /* 3F147E88, A03792A6 */
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7.14072491382608190305e-05, /* 3F12B80F, 32F0A7E9 */
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-1.85586374855275456654e-05, /* BEF375CB, DB605373 */
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2.59073051863633712884e-05, /* 3EFB2A70, 74BF7AD4 */
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/* one */ 1.00000000000000000000e+00, /* 3FF00000, 00000000 */
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/* pio4 */ 7.85398163397448278999e-01, /* 3FE921FB, 54442D18 */
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/* pio4lo */ 3.06161699786838301793e-17 /* 3C81A626, 33145C07 */
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};
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#define one xxx[13]
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#define pio4 xxx[14]
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#define pio4lo xxx[15]
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#define T xxx
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/* INDENT ON */
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double
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__kernel_tan(double x, double y, int iy)
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{
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double z, r, v, w, s;
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int32_t ix, hx;
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GET_HIGH_WORD(hx, x);
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ix = hx & 0x7fffffff; /* high word of |x| */
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if (ix >= 0x3FE59428) { /* |x| >= 0.6744 */
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if (hx < 0) {
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x = -x;
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y = -y;
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}
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z = pio4 - x;
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w = pio4lo - y;
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x = z + w;
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y = 0.0;
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}
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z = x * x;
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w = z * z;
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/*
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* Break x^5*(T[1]+x^2*T[2]+...) into
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* x^5(T[1]+x^4*T[3]+...+x^20*T[11]) +
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* x^5(x^2*(T[2]+x^4*T[4]+...+x^22*[T12]))
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*/
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r = T[1] + w * (T[3] + w * (T[5] + w * (T[7] + w * (T[9] + w * T[11]))));
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v = z * (T[2] + w * (T[4] + w * (T[6] + w * (T[8] + w * (T[10] + w * T[12])))));
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s = z * x;
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r = y + z * (s * (r + v) + y);
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r += T[0] * s;
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w = x + r;
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if (ix >= 0x3FE59428) {
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v = (double)iy;
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return (double)(1 - ((hx >> 30) & 2)) *
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(v - 2.0 * (x - (w * w / (w + v) - r)));
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}
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if (iy == 1)
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return w;
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else {
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/*
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* if allow error up to 2 ulp, simply return
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* -1.0 / (x+r) here
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*/
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/* compute -1.0 / (x+r) accurately */
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double a, t;
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z = w;
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SET_LOW_WORD(z, 0);
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v = r - (z - x); /* z+v = r+x */
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t = a = -1.0 / w; /* a = -1.0/w */
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SET_LOW_WORD(t, 0);
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s = 1.0 + t * z;
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return t + a * (s + t * v);
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}
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}
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