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  1.  
  2. /* @(#)s_atan.c 5.1 93/09/24 */
  3. /*
  4.  * ====================================================
  5.  * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
  6.  *
  7.  * Developed at SunPro, a Sun Microsystems, Inc. business.
  8.  * Permission to use, copy, modify, and distribute this
  9.  * software is freely granted, provided that this notice
  10.  * is preserved.
  11.  * ====================================================
  12.  *
  13.  */
  14.  
  15. /*
  16. FUNCTION
  17.         <<atan>>, <<atanf>>---arc tangent
  18.  
  19. INDEX
  20.    atan
  21. INDEX
  22.    atanf
  23.  
  24. ANSI_SYNOPSIS
  25.         #include <math.h>
  26.         double atan(double <[x]>);
  27.         float atanf(float <[x]>);
  28.  
  29. TRAD_SYNOPSIS
  30.         #include <math.h>
  31.         double atan(<[x]>);
  32.         double <[x]>;
  33.  
  34.         float atanf(<[x]>);
  35.         float <[x]>;
  36.  
  37. DESCRIPTION
  38.  
  39. <<atan>> computes the inverse tangent (arc tangent) of the input value.
  40.  
  41. <<atanf>> is identical to <<atan>>, save that it operates on <<floats>>.
  42.  
  43. RETURNS
  44. @ifnottex
  45. <<atan>> returns a value in radians, in the range of -pi/2 to pi/2.
  46. @end ifnottex
  47. @tex
  48. <<atan>> returns a value in radians, in the range of $-\pi/2$ to $\pi/2$.
  49. @end tex
  50.  
  51. PORTABILITY
  52. <<atan>> is ANSI C.  <<atanf>> is an extension.
  53.  
  54. */
  55.  
  56. /* atan(x)
  57.  * Method
  58.  *   1. Reduce x to positive by atan(x) = -atan(-x).
  59.  *   2. According to the integer k=4t+0.25 chopped, t=x, the argument
  60.  *      is further reduced to one of the following intervals and the
  61.  *      arctangent of t is evaluated by the corresponding formula:
  62.  *
  63.  *      [0,7/16]      atan(x) = t-t^3*(a1+t^2*(a2+...(a10+t^2*a11)...)
  64.  *      [7/16,11/16]  atan(x) = atan(1/2) + atan( (t-0.5)/(1+t/2) )
  65.  *      [11/16.19/16] atan(x) = atan( 1 ) + atan( (t-1)/(1+t) )
  66.  *      [19/16,39/16] atan(x) = atan(3/2) + atan( (t-1.5)/(1+1.5t) )
  67.  *      [39/16,INF]   atan(x) = atan(INF) + atan( -1/t )
  68.  *
  69.  * Constants:
  70.  * The hexadecimal values are the intended ones for the following
  71.  * constants. The decimal values may be used, provided that the
  72.  * compiler will convert from decimal to binary accurately enough
  73.  * to produce the hexadecimal values shown.
  74.  */
  75.  
  76. #include "fdlibm.h"
  77.  
  78. #ifndef _DOUBLE_IS_32BITS
  79.  
  80. #ifdef __STDC__
  81. static const double atanhi[] = {
  82. #else
  83. static double atanhi[] = {
  84. #endif
  85.   4.63647609000806093515e-01, /* atan(0.5)hi 0x3FDDAC67, 0x0561BB4F */
  86.   7.85398163397448278999e-01, /* atan(1.0)hi 0x3FE921FB, 0x54442D18 */
  87.   9.82793723247329054082e-01, /* atan(1.5)hi 0x3FEF730B, 0xD281F69B */
  88.   1.57079632679489655800e+00, /* atan(inf)hi 0x3FF921FB, 0x54442D18 */
  89. };
  90.  
  91. #ifdef __STDC__
  92. static const double atanlo[] = {
  93. #else
  94. static double atanlo[] = {
  95. #endif
  96.   2.26987774529616870924e-17, /* atan(0.5)lo 0x3C7A2B7F, 0x222F65E2 */
  97.   3.06161699786838301793e-17, /* atan(1.0)lo 0x3C81A626, 0x33145C07 */
  98.   1.39033110312309984516e-17, /* atan(1.5)lo 0x3C700788, 0x7AF0CBBD */
  99.   6.12323399573676603587e-17, /* atan(inf)lo 0x3C91A626, 0x33145C07 */
  100. };
  101.  
  102. #ifdef __STDC__
  103. static const double aT[] = {
  104. #else
  105. static double aT[] = {
  106. #endif
  107.   3.33333333333329318027e-01, /* 0x3FD55555, 0x5555550D */
  108.  -1.99999999998764832476e-01, /* 0xBFC99999, 0x9998EBC4 */
  109.   1.42857142725034663711e-01, /* 0x3FC24924, 0x920083FF */
  110.  -1.11111104054623557880e-01, /* 0xBFBC71C6, 0xFE231671 */
  111.   9.09088713343650656196e-02, /* 0x3FB745CD, 0xC54C206E */
  112.  -7.69187620504482999495e-02, /* 0xBFB3B0F2, 0xAF749A6D */
  113.   6.66107313738753120669e-02, /* 0x3FB10D66, 0xA0D03D51 */
  114.  -5.83357013379057348645e-02, /* 0xBFADDE2D, 0x52DEFD9A */
  115.   4.97687799461593236017e-02, /* 0x3FA97B4B, 0x24760DEB */
  116.  -3.65315727442169155270e-02, /* 0xBFA2B444, 0x2C6A6C2F */
  117.   1.62858201153657823623e-02, /* 0x3F90AD3A, 0xE322DA11 */
  118. };
  119.  
  120. #ifdef __STDC__
  121.         static const double
  122. #else
  123.         static double
  124. #endif
  125. one   = 1.0,
  126. huge   = 1.0e300;
  127.  
  128. #ifdef __STDC__
  129.         double atan(double x)
  130. #else
  131.         double atan(x)
  132.         double x;
  133. #endif
  134. {
  135.         double w,s1,s2,z;
  136.         __int32_t ix,hx,id;
  137.  
  138.         GET_HIGH_WORD(hx,x);
  139.         ix = hx&0x7fffffff;
  140.         if(ix>=0x44100000) {    /* if |x| >= 2^66 */
  141.             __uint32_t low;
  142.             GET_LOW_WORD(low,x);
  143.             if(ix>0x7ff00000||
  144.                 (ix==0x7ff00000&&(low!=0)))
  145.                 return x+x;             /* NaN */
  146.             if(hx>0) return  atanhi[3]+atanlo[3];
  147.             else     return -atanhi[3]-atanlo[3];
  148.         } if (ix < 0x3fdc0000) {        /* |x| < 0.4375 */
  149.             if (ix < 0x3e200000) {      /* |x| < 2^-29 */
  150.                 if(huge+x>one) return x;        /* raise inexact */
  151.             }
  152.             id = -1;
  153.         } else {
  154.         x = fabs(x);
  155.         if (ix < 0x3ff30000) {          /* |x| < 1.1875 */
  156.             if (ix < 0x3fe60000) {      /* 7/16 <=|x|<11/16 */
  157.                 id = 0; x = (2.0*x-one)/(2.0+x);
  158.             } else {                    /* 11/16<=|x|< 19/16 */
  159.                 id = 1; x  = (x-one)/(x+one);
  160.             }
  161.         } else {
  162.             if (ix < 0x40038000) {      /* |x| < 2.4375 */
  163.                 id = 2; x  = (x-1.5)/(one+1.5*x);
  164.             } else {                    /* 2.4375 <= |x| < 2^66 */
  165.                 id = 3; x  = -1.0/x;
  166.             }
  167.         }}
  168.     /* end of argument reduction */
  169.         z = x*x;
  170.         w = z*z;
  171.     /* break sum from i=0 to 10 aT[i]z**(i+1) into odd and even poly */
  172.         s1 = z*(aT[0]+w*(aT[2]+w*(aT[4]+w*(aT[6]+w*(aT[8]+w*aT[10])))));
  173.         s2 = w*(aT[1]+w*(aT[3]+w*(aT[5]+w*(aT[7]+w*aT[9]))));
  174.         if (id<0) return x - x*(s1+s2);
  175.         else {
  176.             z = atanhi[id] - ((x*(s1+s2) - atanlo[id]) - x);
  177.             return (hx<0)? -z:z;
  178.         }
  179. }
  180.  
  181. #endif /* _DOUBLE_IS_32BITS */
  182.