Quelle s_atan.cpp Sprache: C

/* @(#)s_atan.c 5.1 93/09/24 */
/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunPro, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*/

//#include <sys/cdefs.h>
//__FBSDID("$FreeBSD$");

/* atan(x)
* Method
*   1. Reduce x to positive by atan(x) = -atan(-x).
*   2. According to the integer k=4t+0.25 chopped, t=x, the argument
*      is further reduced to one of the following intervals and the
*      arctangent of t is evaluated by the corresponding formula:
*
*      [0,7/16]      atan(x) = t-t^3*(a1+t^2*(a2+...(a10+t^2*a11)...)
*      [7/16,11/16]  atan(x) = atan(1/2) + atan( (t-0.5)/(1+t/2) )
*      [11/16.19/16] atan(x) = atan( 1 ) + atan( (t-1)/(1+t) )
*      [19/16,39/16] atan(x) = atan(3/2) + atan( (t-1.5)/(1+1.5t) )
*      [39/16,INF]   atan(x) = atan(INF) + atan( -1/t )
*
* Constants:
* The hexadecimal values are the intended ones for the following
* constants. The decimal values may be used, provided that the
* compiler will convert from decimal to binary accurately enough
* to produce the hexadecimal values shown.
*/

#include <float.h>

#include "math_private.h"

static const double atanhi[] = {
  4.63647609000806093515e-01, /* atan(0.5)hi 0x3FDDAC67, 0x0561BB4F */
  7.85398163397448278999e-01, /* atan(1.0)hi 0x3FE921FB, 0x54442D18 */
  9.82793723247329054082e-01, /* atan(1.5)hi 0x3FEF730B, 0xD281F69B */
  1.57079632679489655800e+00, /* atan(inf)hi 0x3FF921FB, 0x54442D18 */
};

static const double atanlo[] = {
  2.26987774529616870924e-17, /* atan(0.5)lo 0x3C7A2B7F, 0x222F65E2 */
  3.06161699786838301793e-17, /* atan(1.0)lo 0x3C81A626, 0x33145C07 */
  1.39033110312309984516e-17, /* atan(1.5)lo 0x3C700788, 0x7AF0CBBD */
  6.12323399573676603587e-17, /* atan(inf)lo 0x3C91A626, 0x33145C07 */
};

static const double aT[] = {
  3.33333333333329318027e-01, /* 0x3FD55555, 0x5555550D */
-1.99999999998764832476e-01, /* 0xBFC99999, 0x9998EBC4 */
  1.42857142725034663711e-01, /* 0x3FC24924, 0x920083FF */
-1.11111104054623557880e-01, /* 0xBFBC71C6, 0xFE231671 */
  9.09088713343650656196e-02, /* 0x3FB745CD, 0xC54C206E */
-7.69187620504482999495e-02, /* 0xBFB3B0F2, 0xAF749A6D */
  6.66107313738753120669e-02, /* 0x3FB10D66, 0xA0D03D51 */
-5.83357013379057348645e-02, /* 0xBFADDE2D, 0x52DEFD9A */
  4.97687799461593236017e-02, /* 0x3FA97B4B, 0x24760DEB */
-3.65315727442169155270e-02, /* 0xBFA2B444, 0x2C6A6C2F */
  1.62858201153657823623e-02, /* 0x3F90AD3A, 0xE322DA11 */
};

static const double
one   = 1.0,
huge   = 1.0e300;

double
atan(double x)
{
double w,s1,s2,z;
int32_t ix,hx,id;

GET_HIGH_WORD(hx,x);
ix = hx&0x7fffffff;
if(ix>=0x44100000) { /* if |x| >= 2^66 */
     u_int32_t low;
     GET_LOW_WORD(low,x);
     if(ix>0x7ff00000||
  (ix==0x7ff00000&&(low!=0)))
  return x+x;  /* NaN */
     if(hx>0) return  atanhi[3]+*(volatile double *)&atanlo[3];
     else     return -atanhi[3]-*(volatile double *)&atanlo[3];
} if (ix < 0x3fdc0000) { /* |x| < 0.4375 */
     if (ix < 0x3e400000) { /* |x| < 2^-27 */
  if(huge+x>one) return x; /* raise inexact */
     }
     id = -1;
} else {
x = fabs(x);
if (ix < 0x3ff30000) {  /* |x| < 1.1875 */
     if (ix < 0x3fe60000) { /* 7/16 <=|x|<11/16 */
  id = 0; x = (2.0*x-one)/(2.0+x);
     } else {   /* 11/16<=|x|< 19/16 */
  id = 1; x  = (x-one)/(x+one);
     }
} else {
     if (ix < 0x40038000) { /* |x| < 2.4375 */
  id = 2; x  = (x-1.5)/(one+1.5*x);
     } else {   /* 2.4375 <= |x| < 2^66 */
  id = 3; x  = -1.0/x;
     }
}}
    /* end of argument reduction */
z = x*x;
w = z*z;
    /* break sum from i=0 to 10 aT[i]z**(i+1) into odd and even poly */
s1 = z*(aT[0]+w*(aT[2]+w*(aT[4]+w*(aT[6]+w*(aT[8]+w*aT[10])))));
s2 = w*(aT[1]+w*(aT[3]+w*(aT[5]+w*(aT[7]+w*aT[9]))));
if (id<0) return x - x*(s1+s2);
else {
     z = atanhi[id] - ((x*(s1+s2) - atanlo[id]) - x);
     return (hx<0)? -z:z;
}
}

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