s_atan.c 4.3 KB

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  1. /* @(#)s_atan.c 5.1 93/09/24 */
  2. /*
  3. * ====================================================
  4. * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
  5. *
  6. * Developed at SunPro, a Sun Microsystems, Inc. business.
  7. * Permission to use, copy, modify, and distribute this
  8. * software is freely granted, provided that this notice
  9. * is preserved.
  10. * ====================================================
  11. */
  12. #if defined(LIBM_SCCS) && !defined(lint)
  13. static char rcsid[] = "$NetBSD: s_atan.c,v 1.8 1995/05/10 20:46:45 jtc Exp $";
  14. #endif
  15. /* atan(x)
  16. * Method
  17. * 1. Reduce x to positive by atan(x) = -atan(-x).
  18. * 2. According to the integer k=4t+0.25 chopped, t=x, the argument
  19. * is further reduced to one of the following intervals and the
  20. * arctangent of t is evaluated by the corresponding formula:
  21. *
  22. * [0,7/16] atan(x) = t-t^3*(a1+t^2*(a2+...(a10+t^2*a11)...)
  23. * [7/16,11/16] atan(x) = atan(1/2) + atan( (t-0.5)/(1+t/2) )
  24. * [11/16.19/16] atan(x) = atan( 1 ) + atan( (t-1)/(1+t) )
  25. * [19/16,39/16] atan(x) = atan(3/2) + atan( (t-1.5)/(1+1.5t) )
  26. * [39/16,INF] atan(x) = atan(INF) + atan( -1/t )
  27. *
  28. * Constants:
  29. * The hexadecimal values are the intended ones for the following
  30. * constants. The decimal values may be used, provided that the
  31. * compiler will convert from decimal to binary accurately enough
  32. * to produce the hexadecimal values shown.
  33. */
  34. #include "math.h"
  35. #include "math_private.h"
  36. #ifdef __STDC__
  37. static const double atanhi[] = {
  38. #else
  39. static double atanhi[] = {
  40. #endif
  41. 4.63647609000806093515e-01, /* atan(0.5)hi 0x3FDDAC67, 0x0561BB4F */
  42. 7.85398163397448278999e-01, /* atan(1.0)hi 0x3FE921FB, 0x54442D18 */
  43. 9.82793723247329054082e-01, /* atan(1.5)hi 0x3FEF730B, 0xD281F69B */
  44. 1.57079632679489655800e+00, /* atan(inf)hi 0x3FF921FB, 0x54442D18 */
  45. };
  46. #ifdef __STDC__
  47. static const double atanlo[] = {
  48. #else
  49. static double atanlo[] = {
  50. #endif
  51. 2.26987774529616870924e-17, /* atan(0.5)lo 0x3C7A2B7F, 0x222F65E2 */
  52. 3.06161699786838301793e-17, /* atan(1.0)lo 0x3C81A626, 0x33145C07 */
  53. 1.39033110312309984516e-17, /* atan(1.5)lo 0x3C700788, 0x7AF0CBBD */
  54. 6.12323399573676603587e-17, /* atan(inf)lo 0x3C91A626, 0x33145C07 */
  55. };
  56. #ifdef __STDC__
  57. static const double aT[] = {
  58. #else
  59. static double aT[] = {
  60. #endif
  61. 3.33333333333329318027e-01, /* 0x3FD55555, 0x5555550D */
  62. -1.99999999998764832476e-01, /* 0xBFC99999, 0x9998EBC4 */
  63. 1.42857142725034663711e-01, /* 0x3FC24924, 0x920083FF */
  64. -1.11111104054623557880e-01, /* 0xBFBC71C6, 0xFE231671 */
  65. 9.09088713343650656196e-02, /* 0x3FB745CD, 0xC54C206E */
  66. -7.69187620504482999495e-02, /* 0xBFB3B0F2, 0xAF749A6D */
  67. 6.66107313738753120669e-02, /* 0x3FB10D66, 0xA0D03D51 */
  68. -5.83357013379057348645e-02, /* 0xBFADDE2D, 0x52DEFD9A */
  69. 4.97687799461593236017e-02, /* 0x3FA97B4B, 0x24760DEB */
  70. -3.65315727442169155270e-02, /* 0xBFA2B444, 0x2C6A6C2F */
  71. 1.62858201153657823623e-02, /* 0x3F90AD3A, 0xE322DA11 */
  72. };
  73. #ifdef __STDC__
  74. static const double
  75. #else
  76. static double
  77. #endif
  78. one = 1.0,
  79. huge = 1.0e300;
  80. #ifdef __STDC__
  81. double atan(double x)
  82. #else
  83. double atan(x)
  84. double x;
  85. #endif
  86. {
  87. double w,s1,s2,z;
  88. int32_t ix,hx,id;
  89. GET_HIGH_WORD(hx,x);
  90. ix = hx&0x7fffffff;
  91. if(ix>=0x44100000) { /* if |x| >= 2^66 */
  92. u_int32_t low;
  93. GET_LOW_WORD(low,x);
  94. if(ix>0x7ff00000||
  95. (ix==0x7ff00000&&(low!=0)))
  96. return x+x; /* NaN */
  97. if(hx>0) return atanhi[3]+atanlo[3];
  98. else return -atanhi[3]-atanlo[3];
  99. } if (ix < 0x3fdc0000) { /* |x| < 0.4375 */
  100. if (ix < 0x3e200000) { /* |x| < 2^-29 */
  101. if(huge+x>one) return x; /* raise inexact */
  102. }
  103. id = -1;
  104. } else {
  105. x = fabs(x);
  106. if (ix < 0x3ff30000) { /* |x| < 1.1875 */
  107. if (ix < 0x3fe60000) { /* 7/16 <=|x|<11/16 */
  108. id = 0; x = (2.0*x-one)/(2.0+x);
  109. } else { /* 11/16<=|x|< 19/16 */
  110. id = 1; x = (x-one)/(x+one);
  111. }
  112. } else {
  113. if (ix < 0x40038000) { /* |x| < 2.4375 */
  114. id = 2; x = (x-1.5)/(one+1.5*x);
  115. } else { /* 2.4375 <= |x| < 2^66 */
  116. id = 3; x = -1.0/x;
  117. }
  118. }}
  119. /* end of argument reduction */
  120. z = x*x;
  121. w = z*z;
  122. /* break sum from i=0 to 10 aT[i]z**(i+1) into odd and even poly */
  123. s1 = z*(aT[0]+w*(aT[2]+w*(aT[4]+w*(aT[6]+w*(aT[8]+w*aT[10])))));
  124. s2 = w*(aT[1]+w*(aT[3]+w*(aT[5]+w*(aT[7]+w*aT[9]))));
  125. if (id<0) return x - x*(s1+s2);
  126. else {
  127. z = atanhi[id] - ((x*(s1+s2) - atanlo[id]) - x);
  128. return (hx<0)? -z:z;
  129. }
  130. }
  131. libm_hidden_def(atan)