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annotate src/libm/s_atan.c @ 5018:342b158efbbe

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Michael gave permission to use his test code
author Sam Lantinga <slouken@libsdl.org>
date Tue, 18 Jan 2011 10:57:28 -0800
parents 67ad1c88dda0
children
rev   line source
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1 /*
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2 * ====================================================
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3 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
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4 *
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5 * Developed at SunPro, a Sun Microsystems, Inc. business.
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6 * Permission to use, copy, modify, and distribute this
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7 * software is freely granted, provided that this notice
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8 * is preserved.
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9 * ====================================================
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10 */
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11
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12 /* atan(x)
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13 * Method
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14 * 1. Reduce x to positive by atan(x) = -atan(-x).
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15 * 2. According to the integer k=4t+0.25 chopped, t=x, the argument
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16 * is further reduced to one of the following intervals and the
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17 * arctangent of t is evaluated by the corresponding formula:
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18 *
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19 * [0,7/16] atan(x) = t-t^3*(a1+t^2*(a2+...(a10+t^2*a11)...)
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20 * [7/16,11/16] atan(x) = atan(1/2) + atan( (t-0.5)/(1+t/2) )
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21 * [11/16.19/16] atan(x) = atan( 1 ) + atan( (t-1)/(1+t) )
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22 * [19/16,39/16] atan(x) = atan(3/2) + atan( (t-1.5)/(1+1.5t) )
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23 * [39/16,INF] atan(x) = atan(INF) + atan( -1/t )
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24 *
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25 * Constants:
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26 * The hexadecimal values are the intended ones for the following
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27 * constants. The decimal values may be used, provided that the
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28 * compiler will convert from decimal to binary accurately enough
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29 * to produce the hexadecimal values shown.
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30 */
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31
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32 #include "math.h"
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33 #include "math_private.h"
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34
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35 static const double atanhi[] = {
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36 4.63647609000806093515e-01, /* atan(0.5)hi 0x3FDDAC67, 0x0561BB4F */
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37 7.85398163397448278999e-01, /* atan(1.0)hi 0x3FE921FB, 0x54442D18 */
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38 9.82793723247329054082e-01, /* atan(1.5)hi 0x3FEF730B, 0xD281F69B */
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39 1.57079632679489655800e+00, /* atan(inf)hi 0x3FF921FB, 0x54442D18 */
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40 };
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41
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42 static const double atanlo[] = {
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43 2.26987774529616870924e-17, /* atan(0.5)lo 0x3C7A2B7F, 0x222F65E2 */
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44 3.06161699786838301793e-17, /* atan(1.0)lo 0x3C81A626, 0x33145C07 */
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45 1.39033110312309984516e-17, /* atan(1.5)lo 0x3C700788, 0x7AF0CBBD */
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46 6.12323399573676603587e-17, /* atan(inf)lo 0x3C91A626, 0x33145C07 */
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47 };
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48
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49 static const double aT[] = {
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50 3.33333333333329318027e-01, /* 0x3FD55555, 0x5555550D */
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51 -1.99999999998764832476e-01, /* 0xBFC99999, 0x9998EBC4 */
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52 1.42857142725034663711e-01, /* 0x3FC24924, 0x920083FF */
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53 -1.11111104054623557880e-01, /* 0xBFBC71C6, 0xFE231671 */
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54 9.09088713343650656196e-02, /* 0x3FB745CD, 0xC54C206E */
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55 -7.69187620504482999495e-02, /* 0xBFB3B0F2, 0xAF749A6D */
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56 6.66107313738753120669e-02, /* 0x3FB10D66, 0xA0D03D51 */
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57 -5.83357013379057348645e-02, /* 0xBFADDE2D, 0x52DEFD9A */
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58 4.97687799461593236017e-02, /* 0x3FA97B4B, 0x24760DEB */
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59 -3.65315727442169155270e-02, /* 0xBFA2B444, 0x2C6A6C2F */
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60 1.62858201153657823623e-02, /* 0x3F90AD3A, 0xE322DA11 */
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61 };
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62
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63 static const double
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64 one = 1.0,
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65 huge = 1.0e300;
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66
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67 double atan(double x)
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68 {
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69 double w,s1,s2,z;
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70 int32_t ix,hx,id;
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71
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72 GET_HIGH_WORD(hx,x);
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73 ix = hx&0x7fffffff;
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74 if(ix>=0x44100000) { /* if |x| >= 2^66 */
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75 u_int32_t low;
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76 GET_LOW_WORD(low,x);
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77 if(ix>0x7ff00000||
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78 (ix==0x7ff00000&&(low!=0)))
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79 return x+x; /* NaN */
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80 if(hx>0) return atanhi[3]+atanlo[3];
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81 else return -atanhi[3]-atanlo[3];
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82 } if (ix < 0x3fdc0000) { /* |x| < 0.4375 */
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83 if (ix < 0x3e200000) { /* |x| < 2^-29 */
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84 if(huge+x>one) return x; /* raise inexact */
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85 }
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86 id = -1;
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87 } else {
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88 x = fabs(x);
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89 if (ix < 0x3ff30000) { /* |x| < 1.1875 */
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90 if (ix < 0x3fe60000) { /* 7/16 <=|x|<11/16 */
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91 id = 0; x = (2.0*x-one)/(2.0+x);
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92 } else { /* 11/16<=|x|< 19/16 */
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93 id = 1; x = (x-one)/(x+one);
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94 }
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95 } else {
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96 if (ix < 0x40038000) { /* |x| < 2.4375 */
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97 id = 2; x = (x-1.5)/(one+1.5*x);
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98 } else { /* 2.4375 <= |x| < 2^66 */
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99 id = 3; x = -1.0/x;
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100 }
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101 }}
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102 /* end of argument reduction */
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103 z = x*x;
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104 w = z*z;
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105 /* break sum from i=0 to 10 aT[i]z**(i+1) into odd and even poly */
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106 s1 = z*(aT[0]+w*(aT[2]+w*(aT[4]+w*(aT[6]+w*(aT[8]+w*aT[10])))));
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107 s2 = w*(aT[1]+w*(aT[3]+w*(aT[5]+w*(aT[7]+w*aT[9]))));
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108 if (id<0) return x - x*(s1+s2);
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109 else {
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110 z = atanhi[id] - ((x*(s1+s2) - atanlo[id]) - x);
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111 return (hx<0)? -z:z;
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112 }
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113 }
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114 libm_hidden_def(atan)