s_atan.c 3.9 KB

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