1 | |
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2 | /* @(#)s_tan.c 5.1 93/09/24 */ |
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3 | /* |
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4 | * ==================================================== |
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5 | * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. |
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6 | * |
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7 | * Developed at SunPro, a Sun Microsystems, Inc. business. |
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8 | * Permission to use, copy, modify, and distribute this |
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9 | * software is freely granted, provided that this notice |
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10 | * is preserved. |
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11 | * ==================================================== |
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12 | */ |
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13 | |
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14 | |
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15 | /* |
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16 | |
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17 | FUNCTION |
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18 | <<tan>>, <<tanf>>---tangent |
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19 | |
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20 | INDEX |
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21 | tan |
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22 | INDEX |
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23 | tanf |
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24 | |
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25 | SYNOPSIS |
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26 | #include <math.h> |
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27 | double tan(double <[x]>); |
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28 | float tanf(float <[x]>); |
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29 | |
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30 | DESCRIPTION |
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31 | <<tan>> computes the tangent of the argument <[x]>. |
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32 | Angles are specified in radians. |
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33 | |
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34 | <<tanf>> is identical, save that it takes and returns <<float>> values. |
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35 | |
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36 | RETURNS |
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37 | The tangent of <[x]> is returned. |
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38 | |
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39 | PORTABILITY |
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40 | <<tan>> is ANSI. <<tanf>> is an extension. |
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41 | */ |
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42 | |
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43 | /* tan(x) |
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44 | * Return tangent function of x. |
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45 | * |
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46 | * kernel function: |
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47 | * __kernel_tan ... tangent function on [-pi/4,pi/4] |
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48 | * __ieee754_rem_pio2 ... argument reduction routine |
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49 | * |
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50 | * Method. |
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51 | * Let S,C and T denote the sin, cos and tan respectively on |
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52 | * [-PI/4, +PI/4]. Reduce the argument x to y1+y2 = x-k*pi/2 |
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53 | * in [-pi/4 , +pi/4], and let n = k mod 4. |
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54 | * We have |
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55 | * |
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56 | * n sin(x) cos(x) tan(x) |
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57 | * ---------------------------------------------------------- |
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58 | * 0 S C T |
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59 | * 1 C -S -1/T |
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60 | * 2 -S -C T |
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61 | * 3 -C S -1/T |
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62 | * ---------------------------------------------------------- |
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63 | * |
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64 | * Special cases: |
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65 | * Let trig be any of sin, cos, or tan. |
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66 | * trig(+-INF) is NaN, with signals; |
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67 | * trig(NaN) is that NaN; |
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68 | * |
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69 | * Accuracy: |
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70 | * TRIG(x) returns trig(x) nearly rounded |
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71 | */ |
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72 | |
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73 | #include "fdlibm.h" |
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74 | |
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75 | #ifndef _DOUBLE_IS_32BITS |
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76 | |
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77 | #ifdef __STDC__ |
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78 | double tan(double x) |
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79 | #else |
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80 | double tan(x) |
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81 | double x; |
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82 | #endif |
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83 | { |
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84 | double y[2],z=0.0; |
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85 | __int32_t n,ix; |
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86 | |
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87 | /* High word of x. */ |
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88 | GET_HIGH_WORD(ix,x); |
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89 | |
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90 | /* |x| ~< pi/4 */ |
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91 | ix &= 0x7fffffff; |
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92 | if(ix <= 0x3fe921fb) return __kernel_tan(x,z,1); |
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93 | |
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94 | /* tan(Inf or NaN) is NaN */ |
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95 | else if (ix>=0x7ff00000) return x-x; /* NaN */ |
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96 | |
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97 | /* argument reduction needed */ |
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98 | else { |
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99 | n = __ieee754_rem_pio2(x,y); |
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100 | return __kernel_tan(y[0],y[1],1-((n&1)<<1)); /* 1 -- n even |
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101 | -1 -- n odd */ |
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102 | } |
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103 | } |
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104 | |
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105 | #endif /* _DOUBLE_IS_32BITS */ |
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