s_atan.c File Reference

#include "math_libm.h"
#include "math_private.h"

Include dependency graph for s_atan.c:

Go to the source code of this file.

Functions
double	atan (double x)

Variables
static const double	atanhi []
static const double	atanlo []
static const double	aT []
static const double	one = 1.0
static const double	huge = 1.0e300

Function Documentation

double atan

(

double

x

)

Definition at line 67 of file s_atan.c.

References aT, atanhi, atanlo, fabs(), GET_HIGH_WORD, GET_LOW_WORD, huge, and one.

Referenced by __ieee754_atan2(), and SDL_atan().

{
        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]+atanlo[3];
            else     return -atanhi[3]-atanlo[3];
        } if (ix < 0x3fdc0000) {        /* |x| < 0.4375 */
            if (ix < 0x3e200000) {      /* |x| < 2^-29 */
                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;
        }
}

Variable Documentation

const double aT[]

static

Initial value:

 {
  3.33333333333329318027e-01, 
 -1.99999999998764832476e-01, 
  1.42857142725034663711e-01, 
 -1.11111104054623557880e-01, 
  9.09088713343650656196e-02, 
 -7.69187620504482999495e-02, 
  6.66107313738753120669e-02, 
 -5.83357013379057348645e-02, 
  4.97687799461593236017e-02, 
 -3.65315727442169155270e-02, 
  1.62858201153657823623e-02, 
}

Definition at line 49 of file s_atan.c.

Referenced by atan().

const double atanhi[]

static

Initial value:

 {
  4.63647609000806093515e-01, 
  7.85398163397448278999e-01, 
  9.82793723247329054082e-01, 
  1.57079632679489655800e+00, 
}

Definition at line 35 of file s_atan.c.

Referenced by atan().

const double atanlo[]

static

Initial value:

 {
  2.26987774529616870924e-17, 
  3.06161699786838301793e-17, 
  1.39033110312309984516e-17, 
  6.12323399573676603587e-17, 
}

Definition at line 42 of file s_atan.c.

Referenced by atan().

const double huge = 1.0e300

static

Definition at line 65 of file s_atan.c.

Referenced by atan().

const double one = 1.0

static

Definition at line 64 of file s_atan.c.

Referenced by atan().