1 | /* origin: FreeBSD /usr/src/lib/msun/src/s_tan.c */
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2 | /*
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3 | * ====================================================
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4 | * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
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5 | *
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6 | * Developed at SunPro, a Sun Microsystems, Inc. business.
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7 | * Permission to use, copy, modify, and distribute this
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8 | * software is freely granted, provided that this notice
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9 | * is preserved.
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10 | * ====================================================
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11 | */
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12 | /* tan(x)
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13 | * Return tangent function of x.
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14 | *
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15 | * kernel function:
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16 | * __tan ... tangent function on [-pi/4,pi/4]
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17 | * __rem_pio2 ... argument reduction routine
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18 | *
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19 | * Method.
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20 | * Let S,C and T denote the sin, cos and tan respectively on
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21 | * [-PI/4, +PI/4]. Reduce the argument x to y1+y2 = x-k*pi/2
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22 | * in [-pi/4 , +pi/4], and let n = k mod 4.
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23 | * We have
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24 | *
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25 | * n sin(x) cos(x) tan(x)
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26 | * ----------------------------------------------------------
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27 | * 0 S C T
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28 | * 1 C -S -1/T
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29 | * 2 -S -C T
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30 | * 3 -C S -1/T
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31 | * ----------------------------------------------------------
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32 | *
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33 | * Special cases:
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34 | * Let trig be any of sin, cos, or tan.
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35 | * trig(+-INF) is NaN, with signals;
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36 | * trig(NaN) is that NaN;
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37 | *
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38 | * Accuracy:
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39 | * TRIG(x) returns trig(x) nearly rounded
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40 | */
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41 |
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42 | #include "libm.h"
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43 |
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44 | double tan(double x)
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45 | {
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46 | double y[2];
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47 | uint32_t ix;
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48 | unsigned n;
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49 |
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50 | GET_HIGH_WORD(ix, x);
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51 | ix &= 0x7fffffff;
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52 |
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53 | /* |x| ~< pi/4 */
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54 | if (ix <= 0x3fe921fb) {
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55 | if (ix < 0x3e400000) { /* |x| < 2**-27 */
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56 | /* raise inexact if x!=0 and underflow if subnormal */
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57 | FORCE_EVAL(ix < 0x00100000 ? x/0x1p120f : x+0x1p120f);
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58 | return x;
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59 | }
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60 | return __tan(x, 0.0, 0);
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61 | }
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62 |
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63 | /* tan(Inf or NaN) is NaN */
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64 | if (ix >= 0x7ff00000)
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65 | return x - x;
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66 |
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67 | /* argument reduction */
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68 | n = __rem_pio2(x, y);
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69 | return __tan(y[0], y[1], n&1);
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70 | }
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